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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')
plotted figure

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')
plotted figure