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ComparativeAnalysis_ProbabilitesAndMoments

This document contains the codes used to obtain the results of our study. It is divided in two sections: "procedures" and "results". Both sections is organized in two subsections, respectively, an Externally Regulating Gene (ERG) and a Self-Repressing Gene (SRG) models. In "procedures" we find the codes that compute the points for the graphs, and in "results" is shown, properly, the graphs of our work.  

Procedures 

ERG 

The KummerM function parameters are written as functions of the kinetic parameters of the stochastic model for an ERG: 

> a = `/`(`*`(f), `*`(rho)), b = `/`(`*`(`+`(f, h2)), `*`(rho)), N = `/`(`*`(k), `*`(rho)); 1
 

a = `/`(`*`(f), `*`(rho)), b = `/`(`*`(`+`(f, h2)), `*`(rho)), N = `/`(`*`(k), `*`(rho)) (1.1.1)
 

Probabilities 

Here we define the formulas for computing the probabilities phi_n, alpha_n, beta_n as function of the KummerM function parameters: a, b, N. 

> PhinE := `/`(`*`(pochhammer(a, n), `*`(`^`(N, n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(N)))))), `*`(pochhammer(b, n), `*`(factorial(n)))); -1; AlphanE := `/`(`*`(a, `*`(pochhammer(`+`(a, 1), n), ...
PhinE := `/`(`*`(pochhammer(a, n), `*`(`^`(N, n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(N)))))), `*`(pochhammer(b, n), `*`(factorial(n)))); -1; AlphanE := `/`(`*`(a, `*`(pochhammer(`+`(a, 1), n), ...
PhinE := `/`(`*`(pochhammer(a, n), `*`(`^`(N, n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(N)))))), `*`(pochhammer(b, n), `*`(factorial(n)))); -1; AlphanE := `/`(`*`(a, `*`(pochhammer(`+`(a, 1), n), ...
PhinE := `/`(`*`(pochhammer(a, n), `*`(`^`(N, n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(N)))))), `*`(pochhammer(b, n), `*`(factorial(n)))); -1; AlphanE := `/`(`*`(a, `*`(pochhammer(`+`(a, 1), n), ...
 

We compute the probabilities phi_n, alpha_n, beta_n for given values of the KummerM function parameters.
The parameter K gives the maximal value for n and is choosen to ensure that phi0+phi1+...+phiK~1 

> PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
PrE := proc (N1, A, B, rho, K, report) local j, pnts, palpha, nmean, fano, cov, k, f, h2; pnts := [seq([j, evalf(subs(n = j, subs(a = A, b = B, N = N1, AlphanE))), evalf(subs(n = j, subs(a = A, b = B,...
 

Following, we have an example for test the probabilities procedure: 

> Digits := 20; -1
 

> Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 150; -1; Report := false; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], ...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. 0.6e-1]); 1
 

Plot_2d
 

Pearson correlation 

In a ERG, the Pearson correlation between number of proteins n and auxiliar random variable of state gene promoter for given values of the KummerM function parameters is computed by: 

> R := `/`(`*`(sqrt(`/`(`*`(N, `*`(`+`(1, `-`(p)))), `*`(`+`(1, b, `*`(N, `*`(`+`(1, `-`(p))))))))), `*`(sqrt(`+`(b, 1)))); -1
 

> CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
CorrE := proc (N1, B, npnts) local step, palpha, pnts; step := evalf(`/`(1, `*`(npnts))); palpha := [seq(`*`(step, `*`(i)), i = 1 .. npnts)]; pnts := [seq([palpha[i], evalf(subs(N = 50, b = B, p = pal...
 

In this example below, we can test the correlation procedure: 

> Digits := 20; -1
 

> Nf2a := 50; -1; Bf2a := .1; -1; npntsf2a := 1000; -1; corrf2a := []; -1; corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a, npntsf2a)]; -1
Nf2a := 50; -1; Bf2a := .1; -1; npntsf2a := 1000; -1; corrf2a := []; -1; corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a, npntsf2a)]; -1
Nf2a := 50; -1; Bf2a := .1; -1; npntsf2a := 1000; -1; corrf2a := []; -1; corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a, npntsf2a)]; -1
 

> plot(corrf2a, view = [0 .. 1, 0 .. 1]); 1
 

Plot_2d
 

SRG 

For an SRG, the KummerM function parameters are written as functions of the kinetic parameters of the stochastic model as follows: 

> a = `/`(`*`(f), `*`(rho)), b = `+`(`/`(`*`(f), `*`(`+`(rho, h1))), `/`(`*`(N, `*`(rho, `*`(h1))), `*`(`^`(`+`(rho, h1), 2)))), N = `/`(`*`(k), `*`(rho)), z0 = `/`(`*`(rho), `*`(`+`(rho, h1))); 1
 

a = `/`(`*`(f), `*`(rho)), b = `+`(`/`(`*`(f), `*`(`+`(rho, h1))), `/`(`*`(N, `*`(rho, `*`(h1))), `*`(`^`(`+`(rho, h1), 2)))), N = `/`(`*`(k), `*`(rho)), z0 = `/`(`*`(rho), `*`(`+`(rho, h1))) (1.2.1)
 

Probabilities 

Here we define the formulas for computing the probabilities phi_n, alpha_n, beta_n as function of the KummerM function parameters: a, b, N, z0: 

> PhinS := `/`(`*`(pochhammer(a, n), `*`(`^`(`*`(N, `*`(z0)), n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(`*`(N, `*`(`^`(z0, 2))))))))), `*`(pochhammer(b, n), `*`(factorial(n), `*`(KummerM(a, b, `*`(N...
PhinS := `/`(`*`(pochhammer(a, n), `*`(`^`(`*`(N, `*`(z0)), n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(`*`(N, `*`(`^`(z0, 2))))))))), `*`(pochhammer(b, n), `*`(factorial(n), `*`(KummerM(a, b, `*`(N...
PhinS := `/`(`*`(pochhammer(a, n), `*`(`^`(`*`(N, `*`(z0)), n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(`*`(N, `*`(`^`(z0, 2))))))))), `*`(pochhammer(b, n), `*`(factorial(n), `*`(KummerM(a, b, `*`(N...
PhinS := `/`(`*`(pochhammer(a, n), `*`(`^`(`*`(N, `*`(z0)), n), `*`(KummerM(`+`(a, n), `+`(b, n), `+`(`-`(`*`(N, `*`(`^`(z0, 2))))))))), `*`(pochhammer(b, n), `*`(factorial(n), `*`(KummerM(a, b, `*`(N...
 

We compute the probabilities phi_n, alpha_n, beta_n for given values of the KummerM function parameters.
The parameter K gives the maximal value for n and is choosen to ensure that phi0+phi1+...+phiK~1 

> PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
PrS := proc (A, B, Z0, rho, K, report) local j, N1, pnts, palpha, nmean, fano, cov, k, f, h1, h1_eff; N1 := `/`(`*`(`+`(B, `-`(`*`(A, `*`(Z0))))), `*`(Z0, `*`(`+`(1, `-`(Z0))))); palpha := `/`(`*`(A, ...
 

Here, we have an example to test the SRG probabilities procedure: 

> Digits := 20; -1
 

> Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.5e-1]); 1
 

Plot_2d
 

> for k1 to 5 do PrS(Af4b[k1], Bf4b[k1], Zf4b[k1], 0.1e-1, Kf4b, false)[2] end do; 1
 

 

 

 

 

14.883141277015899014
34.432222430725472793
60.191394746073296799
83.160974991360776179
14.178734358249156220 (1.2.1.1)
 

Pearson correlation 

In a SRG, we compute the Pearson correlation between number of proteins n and auxiliar random variable of state gene promoter for given values of the KummerM function parameters by the following procedure: 

> CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
CorrS := proc (Z0, B, npnts) local step, A, N1, palpha, nmean, covS, corrS, pnts; step := evalf(`/`(`*`(B), `*`(Z0, `*`(npnts)))); A := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [se...
 

We can to test the SRG correlation procedure in this example below: 

> Digits := 20; -1
 

> zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
zf2 := .45; -1; Bf2 := 100; -1; npntsf2 := 1000; -1; corrf2b := []; -1; corrf2c := []; -1; corr_aux := CorrS(zf2, Bf2, npntsf2); -1; corrf2b := [op(corrf2b), [seq([corr_aux[i][1], corr_aux[i][3]], i =...
 

 

Plot_2d
Plot_2d
 

Fano Factor 

Here we compute the points for Fano Factor in function of: the probability of gene promotor ON state or the protein mean number:  

> FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
FanoS := proc (A, B, npnts) local step, Z0, N1, palpha, nmean, Fano, pnts; step := evalf(`/`(`*`(B), `*`(A, `*`(npnts)))); Z0 := [seq(`*`(step, `*`(i)), i = 1 .. `+`(npnts, `-`(1)))]; N1 := [seq(`/`(`...
 

We can to test the SRG Fano factor procedure in this example below: 

> Digits := 20; -1
 

> Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
Af5 := 500; -1; Bf5 := 0.1e-1; -1; npntsf5 := 1000; -1; fanof5b := []; -1; fanof5c := []; -1; fano_aux := FanoS(Af5, Bf5, npntsf5); -1; fanof5b := [op(fanof5b), [seq([fano_aux[i][1], fano_aux[i][3]], ...
 

 

Plot_2d
Plot_2d
 

Results 

The graphs of correlations, probabilities distributions and Fano factor, the statistical quantities and the kinectic parameters obtained for a ERG and a SRG models are shown in the two subsections below.   

ERG 

Correlation 

> Digits := 20; -1
 

> Nf2a := 50; -1; Bf2a := [.1, 1, 2, 5, 20]; -1; npntsf2a := 1000; -1; corrf2a := []; -1; for i to nops(Bf2a) do corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a[i], npntsf2a)] end do; -1
Nf2a := 50; -1; Bf2a := [.1, 1, 2, 5, 20]; -1; npntsf2a := 1000; -1; corrf2a := []; -1; for i to nops(Bf2a) do corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a[i], npntsf2a)] end do; -1
Nf2a := 50; -1; Bf2a := [.1, 1, 2, 5, 20]; -1; npntsf2a := 1000; -1; corrf2a := []; -1; for i to nops(Bf2a) do corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a[i], npntsf2a)] end do; -1
Nf2a := 50; -1; Bf2a := [.1, 1, 2, 5, 20]; -1; npntsf2a := 1000; -1; corrf2a := []; -1; for i to nops(Bf2a) do corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a[i], npntsf2a)] end do; -1
Nf2a := 50; -1; Bf2a := [.1, 1, 2, 5, 20]; -1; npntsf2a := 1000; -1; corrf2a := []; -1; for i to nops(Bf2a) do corrf2a := [op(corrf2a), CorrE(Nf2a, Bf2a[i], npntsf2a)] end do; -1
 

> plot(corrf2a, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2a, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2a, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2a, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

Plot_2d
 

Quasi-Fano distributions 

> Digits := 20; -1
 

> Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
Nf3c := 50; -1; Af3c := [36, 40, 44, 48, 50]; -1; Bf3c := 50; -1; Kf3c := 100; -1; probsf3c := []; -1; for i to 5 do probsf3c := [op(probsf3c), PrE(Nf3c, Af3c[i], Bf3c, 0.1e-1, Kf3c, false)] end do; -...
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a=36.0000 b=50.0000

#################### Statistical quantities ###########################
P[alpha]=0.720000 <n>=36.0000 Fano=1.274510 cov=9.882353

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.3600 h2= 0.1400

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a=40.0000 b=50.0000

#################### Statistical quantities ###########################
P[alpha]=0.800000 <n>=40.0000 Fano=1.196078 cov=7.843137

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.4000 h2= 0.1000

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a=44.0000 b=50.0000

#################### Statistical quantities ###########################
P[alpha]=0.880000 <n>=44.0000 Fano=1.117647 cov=5.176471

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.4400 h2= 0.0600

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a=48.0000 b=50.0000

#################### Statistical quantities ###########################
P[alpha]=0.960000 <n>=48.0000 Fano=1.039216 cov=1.882353

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.4800 h2= 0.0200

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a=50.0000 b=50.0000

#################### Statistical quantities ###########################
P[alpha]=1.000000 <n>=50.0000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.5000 h2= 0.0000
 

Super-Fano distributions 

> Digits := 20; -1
 

> Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
Nf4c := 50; -1; Af4c := [.3, .5, 1, 1.5, 1.7]; -1; Bf4c := [.5, 1, 2, 3, 20]; -1; Kf4c := 100; -1; probsf4c := []; -1; for i to 5 do probsf4c := [op(probsf4c), PrE(Nf4c, Af4c[i], Bf4c[i], 0.1e-1, Kf4c...
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a= 0.3000 b= 0.5000

#################### Statistical quantities ###########################
P[alpha]=0.600000 <n>=30.0000 Fano=14.333333 cov=400.000000

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.0030 h2= 0.0020

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a= 0.5000 b= 1.0000

#################### Statistical quantities ###########################
P[alpha]=0.500000 <n>=25.0000 Fano=13.500000 cov=312.500000

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.0050 h2= 0.0050

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a= 1.0000 b= 2.0000

#################### Statistical quantities ###########################
P[alpha]=0.500000 <n>=25.0000 Fano=9.333333 cov=208.333333

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.0100 h2= 0.0100

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a= 1.5000 b= 3.0000

#################### Statistical quantities ###########################
P[alpha]=0.500000 <n>=25.0000 Fano=7.250000 cov=156.250000

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.0150 h2= 0.0150

################################################################
################################################################

For the KummerM function parameter values being
N=50.0000 a= 1.7000 b=20.0000

#################### Statistical quantities ###########################
P[alpha]=0.085000 <n>= 4.2500 Fano=3.178571 cov=9.258929

#################### Kinetic parameters ###########################
k= 0.5000 f= 0.0170 h2= 0.1830
 

SRG 

Correlation 

> Digits := 20; -1
 

> zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
zf2 := .45; -1; Bf2 := [0.1e-1, .1, 1, 10, 100]; -1; npntsf2 := 10000; -1; corrf2b := []; -1; corrf2c := []; -1; for i to nops(Bf2) do corr_aux := CorrS(zf2, Bf2[i], npntsf2); corrf2b := [op(corrf2b),...
 

Correlation versus p[alpha]: 

> plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(corrf2b, view = [0 .. 1, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

Plot_2d
 

Typesetting:-delayDotProduct(`*`(Correlation, `*`(versus)), `<,>`(n), true); -1 

> semilogplot(corrf2c, view = [`^`(10, -3) .. 100, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Pea..." align="center" border="0">
semilogplot(corrf2c, view = [`^`(10, -3) .. 100, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Pea..." align="center" border="0">
semilogplot(corrf2c, view = [`^`(10, -3) .. 100, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Pea..." align="center" border="0">
semilogplot(corrf2c, view = [`^`(10, -3) .. 100, -.5 .. .5], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Pea..." align="center" border="0">
 

Plot_2d
 

Fano distributions 

> Digits := 20; -1
 

> Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
Af3a := [10, 20, 30, 40, 50]; -1; Bf3a := [10, 20, 30, 40, 50]; -1; Zf3a := .9; -1; Kf3a := 80; -1; probsf3a := []; -1; for i to 5 do probsf3a := [op(probsf3a), PrS(Af3a[i], Bf3a[i], Zf3a, 0.1e-1, Kf3...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .13], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=   11.1 a=10.0000 b=10.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=10.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.1111 f= 0.1000 h1= 0.0011 h1_eff= 0.0111

################################################################
################################################################

For the KummerM function parameter values being
N=   22.2 a=20.0000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=20.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.2222 f= 0.2000 h1= 0.0011 h1_eff= 0.0222

################################################################
################################################################

For the KummerM function parameter values being
N=   33.3 a=30.0000 b=30.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=30.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.3333 f= 0.3000 h1= 0.0011 h1_eff= 0.0333

################################################################
################################################################

For the KummerM function parameter values being
N=   44.4 a=40.0000 b=40.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=40.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.4444 f= 0.4000 h1= 0.0011 h1_eff= 0.0444

################################################################
################################################################

For the KummerM function parameter values being
N=   55.6 a=50.0000 b=50.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=50.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.5556 f= 0.5000 h1= 0.0011 h1_eff= 0.0556
 

Quasi-Fano distributions 

> Digits := 20; -1
 

> Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
Af3b := [16, 18, 20, 20.7, 21.5]; -1; Bf3b := 20; -1; Zf3b := .9; -1; Kf3b := 80; -1; probsf3b := []; -1; for i to 5 do probsf3b := [op(probsf3b), PrS(Af3b[i], Bf3b, Zf3b, 0.1e-1, Kf3b, false)[1]] end...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 80, 0 .. .155], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=   62.2 a=16.0000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.753025 <n>=46.8549 Fano=1.373870 cov=17.517657

#################### Kinetic parameters ############################
k= 0.6222 f= 0.1600 h1= 0.0011 h1_eff= 0.0622

################################################################
################################################################

For the KummerM function parameter values being
N=   42.2 a=18.0000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.822842 <n>=34.7422 Fano=1.136361 cov=4.737475

#################### Kinetic parameters ############################
k= 0.4222 f= 0.1800 h1= 0.0011 h1_eff= 0.0422

################################################################
################################################################

For the KummerM function parameter values being
N=   22.2 a=20.0000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.900000 <n>=20.0000 Fano=1.000000 cov=-0.000000

#################### Kinetic parameters ############################
k= 0.2222 f= 0.2000 h1= 0.0011 h1_eff= 0.0222

################################################################
################################################################

For the KummerM function parameter values being
N=   15.2 a=20.7000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.929506 <n>=14.1491 Fano=0.979890 cov=-0.284538

#################### Kinetic parameters ############################
k= 0.1522 f= 0.2070 h1= 0.0011 h1_eff= 0.0152

################################################################
################################################################

For the KummerM function parameter values being
N=    7.2 a=21.5000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.965328 <n>= 6.9718 Fano=0.978236 cov=-0.151733

#################### Kinetic parameters ############################
k= 0.0722 f= 0.2150 h1= 0.0011 h1_eff= 0.0072
 

Super-Fano distributions 

Graph with b fixed 

> Digits := 20; -1
 

> Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
Af4a := [1.2, 1.0, .8, .8, .8]; -1; Bf4a := 2; -1; Zf4a := [.99, .99, .99, .98, .97]; -1; Kf4a := 150; -1; probsf4a := []; -1; for i to 5 do probsf4a := [op(probsf4a), PrS(Af4a[i], Bf4a, Zf4a[i], 0.1e...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.3e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=   82.0 a= 1.2000 b= 2.0000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.655173 <n>=53.7374 Fano=9.788682 cov=472.281200

#################### Kinetic parameters ############################
k= 0.8202 f= 0.0120 h1= 0.0001 h1_eff= 0.0082

################################################################
################################################################

For the KummerM function parameter values being
N=  102.0 a= 1.0000 b= 2.0000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.576942 <n>=58.8597 Fano=14.734677 cov=808.419339

#################### Kinetic parameters ############################
k= 1.0202 f= 0.0100 h1= 0.0001 h1_eff= 0.0102

################################################################
################################################################

For the KummerM function parameter values being
N=  122.0 a= 0.8000 b= 2.0000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.495255 <n>=60.4312 Fano=21.286357 cov=1225.927970

#################### Kinetic parameters ############################
k= 1.2202 f= 0.0080 h1= 0.0001 h1_eff= 0.0122

################################################################
################################################################

For the KummerM function parameter values being
N=   62.0 a= 0.8000 b= 2.0000 z0= 0.9800

#################### Statistical quantities ###########################
P[alpha]=0.490911 <n>=30.4565 Fano=11.194947 cov=310.502815

#################### Kinetic parameters ############################
k= 0.6204 f= 0.0080 h1= 0.0002 h1_eff= 0.0124

################################################################
################################################################

For the KummerM function parameter values being
N=   42.1 a= 0.8000 b= 2.0000 z0= 0.9700

#################### Statistical quantities ###########################
P[alpha]=0.486554 <n>=20.4654 Fano=7.830994 cov=139.798719

#################### Kinetic parameters ############################
k= 0.4206 f= 0.0080 h1= 0.0003 h1_eff= 0.0126
 

Graph without fixed parameter  

> Digits := 20; -1
 

> Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
Af4b := [.38, .6, .75, 1.75, .3]; -1; Bf4b := [.6, 1.2, 2, 3, 20]; -1; Zf4b := [.99, .99, .99, .99, .9]; -1; Kf4b := 150; -1; probsf4b := []; -1; for i to 5 do probsf4b := [op(probsf4b), PrS(Af4b[i], ...
 

> plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot([seq(g[k1], k1 = 1 .. 5)], view = [0 .. 150, 0 .. 0.51e-1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

 

Plot_2d
################################################################
################################################################

For the KummerM function parameter values being
N=   22.6 a= 0.3800 b= 0.6000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.658370 <n>=14.8831 Fano=5.638022 cov=69.028331

#################### Kinetic parameters ############################
k= 0.2261 f= 0.0038 h1= 0.0001 h1_eff= 0.0023

################################################################
################################################################

For the KummerM function parameter values being
N=   61.2 a= 0.6000 b= 1.2000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.562507 <n>=34.4322 Fano=12.766538 cov=405.148046

#################### Kinetic parameters ############################
k= 0.6121 f= 0.0060 h1= 0.0001 h1_eff= 0.0061

################################################################
################################################################

For the KummerM function parameter values being
N=  127.0 a= 0.7500 b= 2.0000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.473873 <n>=60.1914 Fano=23.246285 cov=1339.034939

#################### Kinetic parameters ############################
k= 1.2702 f= 0.0075 h1= 0.0001 h1_eff= 0.0127

################################################################
################################################################

For the KummerM function parameter values being
N=  128.0 a= 1.7500 b= 3.0000 z0= 0.9900

#################### Statistical quantities ###########################
P[alpha]=0.649541 <n>=83.1610 Fano=11.315696 cov=857.863321

#################### Kinetic parameters ############################
k= 1.2803 f= 0.0175 h1= 0.0001 h1_eff= 0.0128

################################################################
################################################################

For the KummerM function parameter values being
N=  219.2 a= 0.3000 b=20.0000 z0= 0.9000

#################### Statistical quantities ###########################
P[alpha]=0.064677 <n>=14.1787 Fano=25.866882 cov=352.580909

#################### Kinetic parameters ############################
k= 2.1922 f= 0.0030 h1= 0.0011 h1_eff= 0.2192
 

Sub-Fano distributions 

> Digits := 20; -1
 

> Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
Af5a := [833, 1667, 3333, 5000, 6667]; -1; Bf5a := [.5, 1, 2, 3, 4]; -1; Zf5a := `+`(`*`(5, `*`(`^`(10, -4)))); -1; Kf5a := 100; -1; probsf5a1 := []; -1; nmeanf5a1 := []; -1; probsf5a2 := []; -1; for ...
 

 

Plot_2d

For sub-Fano distributions:
################################################################
################################################################

For the KummerM function parameter values being
N=  167.1 a=833.0000 b= 0.5000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.050183 <n>= 8.3848 Fano=0.502254 cov=-4.173491

#################### Kinetic parameters ############################
k= 1.6708 f= 8.3300 h1=19.9900 h1_eff= 1.6700

################################################################
################################################################

For the KummerM function parameter values being
N=  333.2 a=1667.0000 b= 1.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.049517 <n>=16.4973 Fano=0.509992 cov=-8.083793

#################### Kinetic parameters ############################
k= 3.3317 f=16.6700 h1=19.9900 h1_eff= 3.3300
 

################################################################
################################################################

For the KummerM function parameter values being
N=  667.3 a=3333.0000 b= 2.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.049108 <n>=32.7714 Fano=0.513676 cov=-15.937528

#################### Kinetic parameters ############################
k= 6.6733 f=33.3300 h1=19.9900 h1_eff= 6.6700

################################################################
################################################################

For the KummerM function parameter values being
N= 1000.5 a=5000.0000 b= 3.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.049003 <n>=49.0271 Fano=0.514881 cov=-23.783969

#################### Kinetic parameters ############################
k=10.0050 f=50.0000 h1=19.9900 h1_eff=10.0000

################################################################
################################################################

For the KummerM function parameter values being
N= 1333.7 a=6667.0000 b= 4.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.048950 <n>=65.2833 Fano=0.515480 cov=-31.631067

#################### Kinetic parameters ############################
k=13.3367 f=66.6700 h1=19.9900 h1_eff=13.3300


For Fano distributions:
################################################################
################################################################

For the KummerM function parameter values being
N= 1000.0 a= 0.5000 b= 0.5000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.000500 <n>= 0.5000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ############################
k=10.0000 f= 0.0050 h1=19.9900 h1_eff= 9.9950

################################################################
################################################################

For the KummerM function parameter values being
N= 2000.0 a= 1.0000 b= 1.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.000500 <n>= 1.0000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ############################
k=20.0000 f= 0.0100 h1=19.9900 h1_eff=19.9900

################################################################
################################################################

For the KummerM function parameter values being
N= 4000.0 a= 2.0000 b= 2.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.000500 <n>= 2.0000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ############################
k=40.0000 f= 0.0200 h1=19.9900 h1_eff=39.9800
 

################################################################
################################################################

For the KummerM function parameter values being
N= 6000.0 a= 3.0000 b= 3.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.000500 <n>= 3.0000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ############################
k=60.0000 f= 0.0300 h1=19.9900 h1_eff=59.9700

################################################################
################################################################

For the KummerM function parameter values being
N= 8000.0 a= 4.0000 b= 4.0000 z0= 0.0005

#################### Statistical quantities ###########################
P[alpha]=0.000500 <n>= 4.0000 Fano=1.000000 cov=0.000000

#################### Kinetic parameters ############################
k=80.0000 f= 0.0400 h1=19.9900 h1_eff=79.9600
 

Fano factor 

> Digits := 20; -1
 

> Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
Af5 := 500; -1; Bf5 := [0.1e-1, 0.5e-1, .1, .5, 2]; -1; npntsf5 := 10000; -1; fanof5b := []; -1; fanof5c := []; -1; for i to nops(Bf5) do fano_aux := FanoS(Af5, Bf5[i], npntsf5); fanof5b := [op(fanof5...
 

Fano versus p[alpha]: 

> plot(fanof5b, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(fanof5b, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(fanof5b, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
plot(fanof5b, view = [0 .. 1, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title =
 

Plot_2d
 

Fano versus <n>: 

> plot(fanof5c, view = [0 .. 7, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Fano factor"], labeldirections = ["..." align="center" border="0">
plot(fanof5c, view = [0 .. 7, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Fano factor"], labeldirections = ["..." align="center" border="0">
plot(fanof5c, view = [0 .. 7, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Fano factor"], labeldirections = ["..." align="center" border="0">
plot(fanof5c, view = [0 .. 7, 0 .. 1], color = [red, blue, green, cyan, magenta], thickness = 2, axes = boxed, title = ", "Fano factor"], labeldirections = ["..." align="center" border="0">
 

Plot_2d