The Gaussian Tail Distribution¶

gsl_ran_gaussian_tail
(a, 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 limita
, which must be positive. The method is based on Marsaglia’s famous rectanglewedgetail algorithm (Ann. Math. Stat. 32, 894899 (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,
\[N(a;\sigma) = (1/2) \operatorname{erfc}(a / \sqrt{2 \sigma^2}).\]

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

gsl_ran_ugaussian_tail
(a)¶

gsl_ran_ugaussian_tail_pdf
(x, 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.