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,
\[N(a;\sigma) = (1/2) \operatorname{erfc}(a / \sqrt{2 \sigma^2}).\]