The Bivariate Gaussian Distribution

Random: void gsl_ran_bivariate_gaussian (const gsl_rng * r, double sigma_x, double sigma_y, double rho, double * x, double * y)

This function generates a pair of correlated gaussian variates, with mean zero, correlation coefficient rho and standard deviations sigma_x and sigma_y in the @math{x} and @math{y} directions. The probability distribution for bivariate gaussian random variates is,

for @math{x,y} in the range @math{-\infty} to @math{+\infty}. The correlation coefficient rho should lie between @math{1} and @math{-1}.

Function: double gsl_ran_bivariate_gaussian_pdf (double x, double y, double sigma_x, double sigma_y, double rho)

This function computes the probability density @math{p(x,y)} at (x,y) for a bivariate gaussian distribution with standard deviations sigma_x, sigma_y and correlation coefficient rho, using the formula given above.