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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 19.19 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.

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.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition