Statistics: ncfpdf

### Function Reference: `ncfpdf`

statistics: y = ncfpdf (x, df1, df2, lambda)

Noncentral F-probability density function (PDF).

For each element of x, compute the probability density function (PDF) of the noncentral F-distribution with df1 and df2 degrees of freedom and noncentrality parameter lambda. The size of y 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.

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

See also: ncfcdf, ncfinv, ncfrnd, ncfstat, fpdf

Source Code: ncfpdf

### Example: 1

     ## Plot various PDFs from the noncentral F distribution
     x = 0:0.01:5;
     y1 = ncfpdf (x, 2, 5, 1);
     y2 = ncfpdf (x, 2, 5, 2);
     y3 = ncfpdf (x, 5, 10, 1);
     y4 = ncfpdf (x, 10, 20, 10);
     plot (x, y1, "-r", x, y2, "-g", x, y3, "-k", x, y4, "-m")
     grid on
     xlim ([0, 5])
     ylim ([0, 0.8])
     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", "northeast")
     title ("Noncentral F PDF")
     xlabel ("values in x")
     ylabel ("density")

### Example: 2

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

     x = 0.01:0.1:10.01;
     y1 = ncfpdf (x, 5, 20, 10);
     y2 = fpdf (x, 5, 20);
     plot (x, y1, "-", x, y2, "-");
     grid on
     xlim ([0, 10])
     ylim ([0, 0.8])
     legend ({"Noncentral F(5,20,10)", "F(5,20)"}, "location", "northeast")
     title ("Noncentral F vs F PDFs")
     xlabel ("values in x")
     ylabel ("density")