The Gaussian Tail Distribution¶
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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 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,
\[N(a;\sigma) = (1/2) \operatorname{erfc}(a / \sqrt{2 \sigma^2}).\]
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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
sigmaand lower limita, using the formula given above.
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gsl_ran_ugaussian_tail(a)¶
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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.