Statistics: ncx2inv

### 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")

### 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")