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.
-
gsl_ran_chisq(nu)
This function returns a random variate from chi-squared distribution
with nu degrees 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 \(x \geq 0\).
-
gsl_ran_chisq_pdf(x, nu)
This function computes the probability density \(p(x)\) at \(x\) for a
chi-squared distribution with nu degrees of freedom, using the
formula given above.
-
gsl_ran_chisq_P(x, nu)
-
gsl_ran_chisq_Q(x, nu)
-
gsl_ran_chisq_Pinv(P, nu)
-
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 nu degrees of freedom.