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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")
plotted figure

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")
plotted figure