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