Statistics: nctinv

### Function Reference: `nctinv`

statistics: x = ncx2inv (p, df, mu)

Inverse of the non-central t-cumulative distribution function (iCDF).

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

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

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

See also: nctcdf, nctpdf, nctrnd, nctstat, tinv

Source Code: nctinv

### Example: 1

     ## Plot various iCDFs from the noncentral T distribution
     p = 0.001:0.001:0.999;
     x1 = nctinv (p, 1, 0);
     x2 = nctinv (p, 4, 0);
     x3 = nctinv (p, 1, 2);
     x4 = nctinv (p, 4, 2);
     plot (p, x1, "-r", p, x2, "-g", p, x3, "-k", p, x4, "-m")
     grid on
     ylim ([-5, 5])
     legend ({"df = 1, μ = 0", "df = 4, μ = 0", ...
              "df = 1, μ = 2", "df = 4, μ = 2"}, "location", "northwest")
     title ("Noncentral T iCDF")
     xlabel ("probability")
     ylabel ("values in x")

### Example: 2

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

     p = 0.001:0.001:0.999;
     x1 = nctinv (p, 10, 1);
     x2 = tinv (p, 10);
     plot (p, x1, "-", p, x2, "-");
     grid on
     ylim ([-5, 5])
     legend ({"Noncentral T(10,1)", "T(10)"}, "location", "northwest")
     title ("Noncentral T vs T quantile functions")
     xlabel ("probability")
     ylabel ("values in x")