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Function Reference: ncx2inv

statistics: x = ncx2inv (p, df, lambda)

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

Example: 1

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')
plotted figure

Example: 2

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')
plotted figure