### Function Reference: `nctpdf`

statistics: y = nctpdf (x, df, mu)

Noncentral t-probability density function (PDF).

For each element of x, compute the probability density function (PDF) of the noncentral t-distribution with df degrees of freedom and noncentrality parameter mu. The size of y is the common size of x, df, and mu. A scalar input functions as a constant matrix of the same size as the other inputs.

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

See also: nctcdf, nctinv, nctrnd, nctstat, tpdf

Source Code: nctpdf

### Example: 1

     ## Plot various PDFs from the noncentral T distribution
     x = -5:0.01:10;
     y1 = nctpdf (x, 1, 0);
     y2 = nctpdf (x, 4, 0);
     y3 = nctpdf (x, 1, 2);
     y4 = nctpdf (x, 4, 2);
     plot (x, y1, "-r", x, y2, "-g", x, y3, "-k", x, y4, "-m")
     grid on
     xlim ([-5, 10])
     ylim ([0, 0.4])
     legend ({"df = 1, μ = 0", "df = 4, μ = 0", ...
              "df = 1, μ = 2", "df = 4, μ = 2"}, "location", "northeast")
     title ("Noncentral T PDF")
     xlabel ("values in x")
     ylabel ("density")

### Example: 2

     ## Compare the noncentral T PDF with MU = 1 to the T PDF
     ## with the same number of degrees of freedom (10).

     x = -5:0.1:5;
     y1 = nctpdf (x, 10, 1);
     y2 = tpdf (x, 10);
     plot (x, y1, "-", x, y2, "-");
     grid on
     xlim ([-5, 5])
     ylim ([0, 0.4])
     legend ({"Noncentral χ^2(4,2)", "χ^2(4)"}, "location", "northwest")
     title ("Noncentral T vs T PDFs")
     xlabel ("values in x")
     ylabel ("density")