18.2 The Gaussian Tail Distribution

Random: 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,

p(x) dx = {1 \over N(a;\sigma)} \exp (- x^2/(2 \sigma^2)) dx

for x > a where N(a;\sigma) is the normalization constant,

N(a;\sigma) = (1/2) erfc(a / sqrt(2 sigma^2)).

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.

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

Random: 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.