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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