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.
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gsl_ran_tdist(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 \(-\infty < x < +\infty\).
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gsl_ran_tdist_pdf(x, nu)¶
This function computes the probability density \(p(x)\) at \(x\) for a t-distribution with
nudegrees of freedom, using the formula given above.
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gsl_cdf_tdist_P(x, nu)¶
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gsl_cdf_tdist_Q(x, nu)¶
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gsl_cdf_tdist_Pinv(P, nu)¶
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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
nudegrees of freedom.