Statistics: ncfinv

### Function Reference: `ncfinv`

statistics: x = ncfinv (p, df1, df2, lambda)

Inverse of the noncentral F-cumulative distribution function (iCDF).

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

`ncfinv` uses Newton’s method to converge to the solution.

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

See also: ncfcdf, ncfpdf, ncfrnd, ncfstat, finv

Source Code: ncfinv

### Example: 1

     ## Plot various iCDFs from the noncentral F distribution
     p = 0.001:0.001:0.999;
     x1 = ncfinv (p, 2, 5, 1);
     x2 = ncfinv (p, 2, 5, 2);
     x3 = ncfinv (p, 5, 10, 1);
     x4 = ncfinv (p, 10, 20, 10);
     plot (p, x1, "-r", p, x2, "-g", p, x3, "-k", p, x4, "-m")
     grid on
     ylim ([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", "northwest")
     title ("Noncentral F iCDF")
     xlabel ("probability")
     ylabel ("values in x")

### Example: 2

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

     p = 0.001:0.001:0.999;
     x1 = ncfinv (p, 5, 20, 10);
     x2 = finv (p, 5, 20);
     plot (p, x1, "-", p, x2, "-");
     grid on
     ylim ([0, 10])
     legend ({"Noncentral F(5,20,10)", "F(5,20)"}, "location", "northwest")
     title ("Noncentral F vs F quantile functions")
     xlabel ("probability")
     ylabel ("values in x")