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Function Reference: ncfcdf

statistics: p = ncfcdf (x, df1, df2, lambda)
statistics: p = ncfcdf (x, df1, df2, lambda, 'upper')

Noncentral F-cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the noncentral F-distribution with df1 and df2 degrees of freedom and noncentrality parameter lambda. The size of p is the common size of x, df1, df2, and lambda. A scalar input functions as a constant matrix of the same size as the other inputs.

p = ncfcdf (x, df1, df2, lambda, "upper") computes the upper tail probability of the noncentral F-distribution with parameters df1, df2, and lambda, at the values in x.

Further information about the noncentral F-distribution can be found at https://en.wikipedia.org/wiki/Noncentral_F-distribution

See also: ncfinv, ncfpdf, ncfrnd, ncfstat, fcdf

Source Code: ncfcdf

Example: 1

Plot various CDFs from the noncentral F distribution

 x = 0:0.01:5;
 p1 = ncfcdf (x, 2, 5, 1);
 p2 = ncfcdf (x, 2, 5, 2);
 p3 = ncfcdf (x, 5, 10, 1);
 p4 = ncfcdf (x, 10, 20, 10);
 plot (x, p1, '-r', x, p2, '-g', x, p3, '-k', x, p4, '-m')
 grid on
 xlim ([0, 5])
 legend ({'df1 = 2, df2 = 5, λ = 1', 'df1 = 2, df2 = 5, λ = 2', ...
          'df1 = 5, df2 = 10, λ = 1', 'df1 = 10, df2 = 20, λ = 10'}, ...
         'location', 'southeast')
 title ('Noncentral F CDF')
 xlabel ('values in x')
 ylabel ('probability')
plotted figure

Example: 2

Compare the noncentral F CDF with LAMBDA = 10 to the F CDF with the same number of numerator and denominator degrees of freedom (5, 20)

 x = 0.01:0.1:10.01;
 p1 = ncfcdf (x, 5, 20, 10);
 p2 = fcdf (x, 5, 20);
 plot (x, p1, '-', x, p2, '-');
 grid on
 xlim ([0, 10])
 legend ({'Noncentral F(5,20,10)', 'F(5,20)'}, 'location', 'southeast')
 title ('Noncentral F vs F CDFs')
 xlabel ('values in x')
 ylabel ('probability')
plotted figure