20.18 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.

Function: double gsl_ran_chisq (const gsl_rng * r, double nu)

This function returns a random variate from the 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 >= 0.

Function: double gsl_ran_chisq_pdf (double x, double 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.

Function: double gsl_cdf_chisq_P (double x, double nu)

Function: double gsl_cdf_chisq_Q (double x, double nu)

Function: double gsl_cdf_chisq_Pinv (double P, double nu)

Function: double gsl_cdf_chisq_Qinv (double Q, double 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.