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Function Reference: ncx2cdf

statistics: p = ncx2cdf (x, df, lambda)
statistics: p = ncx2cdf (x, df, lambda, 'upper')

Noncentral chi-squared cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the noncentral chi-squared distribution with df degrees of freedom and noncentrality parameter lambda. The size of p 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.

p = ncx2cdf (x, df, lambda, "upper") computes the upper tail probability of the noncentral chi-squared distribution with parameters df and lambda, at the values in x.

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

See also: ncx2inv, ncx2pdf, ncx2rnd, ncx2stat, chi2cdf

Source Code: ncx2cdf

Example: 1

Plot various CDFs from the noncentral chi-squared distribution

 x = 0:0.1:10;
 p1 = ncx2cdf (x, 2, 1);
 p2 = ncx2cdf (x, 2, 2);
 p3 = ncx2cdf (x, 2, 3);
 p4 = ncx2cdf (x, 4, 1);
 p5 = ncx2cdf (x, 4, 2);
 p6 = ncx2cdf (x, 4, 3);
 plot (x, p1, '-r', x, p2, '-g', x, p3, '-k', ...
       x, p4, '-m', x, p5, '-c', x, p6, '-y')
 grid on
 xlim ([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', 'southeast')
 title ('Noncentral chi-squared CDF')
 xlabel ('values in x')
 ylabel ('probability')
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).

 x = 0:0.1:10;
 p1 = ncx2cdf (x, 4, 2);
 p2 = chi2cdf (x, 4);
 plot (x, p1, '-', x, p2, '-')
 grid on
 xlim ([0, 10])
 legend ({'Noncentral χ^2(4,2)', 'χ^2(4)'}, 'location', 'northwest')
 title ('Noncentral chi-squared vs chi-squared CDFs')
 xlabel ('values in x')
 ylabel ('probability')
plotted figure