19.3 The Gaussian Tail Distribution

Function: double gsl_ran_gaussian_tail (const gsl_rng * r, double a, double sigma)

This function provides random variates from the upper tail of a Gaussian distribution with standard deviation sigma. The values returned are larger than the lower limit a, which must be positive. The method is based on Marsaglia's famous rectangle-wedge-tail algorithm (Ann. Math. Stat. 32, 894–899 (1961)), with this aspect explained in Knuth, v2, 3rd ed, p139,586 (exercise 11).

The probability distribution for Gaussian tail random variates is, for x > a where N(a;\sigma) is the normalization constant,

Function: double gsl_ran_gaussian_tail_pdf (double x, double a, double sigma)

This function computes the probability density p(x) at x for a Gaussian tail distribution with standard deviation sigma and lower limit a, using the formula given above.

Function: double gsl_ran_ugaussian_tail (const gsl_rng * r, double a)

Function: double gsl_ran_ugaussian_tail_pdf (double x, double a)

These functions compute results for the tail of a unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of one, sigma = 1.