nctinv
Inverse of the non-central -cumulative distribution function (iCDF).
For each element of p, compute the quantile (the inverse of the CDF) of the noncentral -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 -distribution can be found at https://en.wikipedia.org/wiki/Noncentral_t-distribution
See also: nctcdf, nctpdf, nctrnd, nctstat, tinv
Source Code: nctinv
## 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")
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## 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")
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