Statistics: ncfcdf

### 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")

### 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")