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Function Reference: nctcdf

statistics: p = nctcdf (x, df, mu)
statistics: p = nctcdf (x, df, mu, 'upper')

Noncentral t-cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the noncentral t-distribution with df degrees of freedom and noncentrality parameter mu. The size of p 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.

p = nctcdf (x, df, mu, "upper") computes the upper tail probability of the noncentral t-distribution with parameters df and mu, at the values in x.

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

See also: nctinv, nctpdf, nctrnd, nctstat, tcdf

Source Code: nctcdf

Example: 1

Plot various CDFs from the noncentral Τ distribution

 x = -5:0.01:5;
 p1 = nctcdf (x, 1, 0);
 p2 = nctcdf (x, 4, 0);
 p3 = nctcdf (x, 1, 2);
 p4 = nctcdf (x, 4, 2);
 plot (x, p1, '-r', x, p2, '-g', x, p3, '-k', x, p4, '-m')
 grid on
 xlim ([-5, 5])
 legend ({'df = 1, μ = 0', 'df = 4, μ = 0', ...
          'df = 1, μ = 2', 'df = 4, μ = 2'}, 'location', 'southeast')
 title ('Noncentral Τ CDF')
 xlabel ('values in x')
 ylabel ('probability')
plotted figure

Example: 2

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

 x = -5:0.1:5;
 p1 = nctcdf (x, 10, 1);
 p2 = tcdf (x, 10);
 plot (x, p1, '-', x, p2, '-')
 grid on
 xlim ([-5, 5])
 legend ({'Noncentral T(10,1)', 'T(10)'}, 'location', 'southeast')
 title ('Noncentral T vs T CDFs')
 xlabel ('values in x')
 ylabel ('probability')
plotted figure