ncx2inv
Inverse of the noncentral chi-squared cumulative distribution function (iCDF).
For each element of p, compute the quantile (the inverse of the CDF) of the noncentral chi-squared distribution with df degrees of freedom and noncentrality parameter mu. The size of x is the common size of p, df, and mu. A scalar input functions as a constant matrix of the same size as the other inputs.
ncx2inv uses Newton’s method to converge to the solution.
Further information about the noncentral chi-squared distribution can be found at https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
See also: ncx2cdf, ncx2pdf, ncx2rnd, ncx2stat, chi2inv
Source Code: ncx2inv
## Plot various iCDFs from the noncentral chi-squared distribution
p = 0.001:0.001:0.999;
x1 = ncx2inv (p, 2, 1);
x2 = ncx2inv (p, 2, 2);
x3 = ncx2inv (p, 2, 3);
x4 = ncx2inv (p, 4, 1);
x5 = ncx2inv (p, 4, 2);
x6 = ncx2inv (p, 4, 3);
plot (p, x1, "-r", p, x2, "-g", p, x3, "-k", ...
p, x4, "-m", p, x5, "-c", p, x6, "-y")
grid on
ylim ([0, 10])
legend ({"df = 2, λ = 1", "df = 2, λ = 2", ...
"df = 2, λ = 3", "df = 4, λ = 1", ...
"df = 4, λ = 2", "df = 4, λ = 3"}, "location", "northwest")
title ("Noncentral chi-squared iCDF")
xlabel ("probability")
ylabel ("values in x")
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## Compare the noncentral chi-squared CDF with LAMBDA = 2 to the
## chi-squared CDF with the same number of degrees of freedom (4).
p = 0.001:0.001:0.999;
x1 = ncx2inv (p, 4, 2);
x2 = chi2inv (p, 4);
plot (p, x1, "-", p, x2, "-");
grid on
ylim ([0, 10])
legend ({"Noncentral χ^2(4,2)", "χ^2(4)"}, "location", "northwest")
title ("Noncentral chi-squared vs chi-squared quantile functions")
xlabel ("probability")
ylabel ("values in x")
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