The t-distribution

The t-distribution arises in statistics. If \(Y_1\) has a normal distribution and \(Y_2\) has a chi-squared distribution with \(\nu\) degrees of freedom then the ratio,

\[X = { Y_1 \over \sqrt{Y_2 / \nu} }\]

has a t-distribution \(t(x;\nu)\) with \(\nu\) degrees of freedom.


This function returns a random variate from the t-distribution. The distribution function is,

\[p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)} (1 + x^2/\nu)^{-(\nu + 1)/2} dx\]

for \(-\infty < x < +\infty\).

gsl_ran_tdist_pdf(x, nu)

This function computes the probability density \(p(x)\) at \(x\) for a t-distribution with nu degrees of freedom, using the formula given above.

gsl_cdf_tdist_P(x, nu)
gsl_cdf_tdist_Q(x, nu)
gsl_cdf_tdist_Pinv(P, nu)
gsl_cdf_tdist_Qinv(Q, nu)

These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the t-distribution with nu degrees of freedom.