Statistics: ncx2pdf

### Function Reference: `ncx2pdf`

statistics: y = ncx2pdf (x, df, lambda)

Noncentral chi-squared probability distribution function (PDF).

For each element of x, compute the probability density function (PDF) of the noncentral chi-squared distribution with df degrees of freedom and noncentrality parameter lambda. The size of y is the common size of x, df, and lambda. A scalar input functions as a constant matrix of the same size as the other inputs.

Further information about the noncentral chi-squared distribution can be found at https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution

See also: ncx2cdf, ncx2inv, ncx2rnd, ncx2stat, chi2pdf

Source Code: ncx2pdf

### Example: 1

     ## Plot various PDFs from the noncentral chi-squared distribution
     x = 0:0.1:10;
     y1 = ncx2pdf (x, 2, 1);
     y2 = ncx2pdf (x, 2, 2);
     y3 = ncx2pdf (x, 2, 3);
     y4 = ncx2pdf (x, 4, 1);
     y5 = ncx2pdf (x, 4, 2);
     y6 = ncx2pdf (x, 4, 3);
     plot (x, y1, "-r", x, y2, "-g", x, y3, "-k", ...
           x, y4, "-m", x, y5, "-c", x, y6, "-y")
     grid on
     xlim ([0, 10])
     ylim ([0, 0.32])
     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", "northeast")
     title ("Noncentral chi-squared PDF")
     xlabel ("values in x")
     ylabel ("density")

### Example: 2

     ## Compare the noncentral chi-squared PDF with LAMBDA = 2 to the
     ## chi-squared PDF with the same number of degrees of freedom (4).

     x = 0:0.1:10;
     y1 = ncx2pdf (x, 4, 2);
     y2 = chi2pdf (x, 4);
     plot (x, y1, "-", x, y2, "-");
     grid on
     xlim ([0, 10])
     ylim ([0, 0.32])
     legend ({"Noncentral T(10,1)", "T(10)"}, "location", "northwest")
     title ("Noncentral chi-squared vs chi-squared PDFs")
     xlabel ("values in x")
     ylabel ("density")