GNU Scientific Library – Reference Manual: The Bivariate Gaussian Distribution

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### 20.4 The Bivariate Gaussian Distribution

Function: 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 x and y directions. The probability distribution for bivariate Gaussian random variates is, for x,y in the range -\infty to +\infty. The correlation coefficient rho should lie between 1 and -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 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.