The Chi-squared Distribution¶
The chi-squared distribution arises in statistics. If \(Y_i\) are \(n\) independent Gaussian random variates with unit variance then the sum-of-squares,
\[X_i = \sum_i Y_i^2\]
has a chi-squared distribution with \(n\) degrees of freedom.
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gsl_ran_chisq(nu)¶
This function returns a random variate from chi-squared distribution with
nudegrees of freedom. The distribution function is,\[p(x) dx = {1 \over 2 \Gamma(\nu/2) } (x/2)^{\nu/2 - 1} \exp(-x/2) dx\]for \(x \geq 0\).
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gsl_ran_chisq_pdf(x, nu)¶
This function computes the probability density \(p(x)\) at \(x\) for a chi-squared distribution with
nudegrees of freedom, using the formula given above.
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gsl_ran_chisq_P(x, nu)¶
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gsl_ran_chisq_Q(x, nu)¶
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gsl_ran_chisq_Pinv(P, nu)¶
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gsl_ran_chisq_Qinv(Q, nu)¶
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the chi-squared distribution with
nudegrees of freedom.