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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 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,

p(x) dx = {1 \over N(a;\sigma) \sqrt{2 \pi \sigma^2}} \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.

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.
 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition