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. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £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 |