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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.

- Function:
*double***gsl_ran_tdist***(const gsl_rng **`r`, double`nu`) -
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*.

- Function:
*double***gsl_ran_tdist_pdf***(double*`x`, double`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.

- Function:
*double***gsl_cdf_tdist_P***(double*`x`, double`nu`) - Function:
*double***gsl_cdf_tdist_Q***(double*`x`, double`nu`) - Function:
*double***gsl_cdf_tdist_Pinv***(double*`P`, double`nu`) - Function:
*double***gsl_cdf_tdist_Qinv***(double*`Q`, double`nu`) These functions compute the cumulative distribution functions

*P(x)*,*Q(x)*and their inverses for the t-distribution with`nu`degrees of freedom.