C. D. F. Andrews. Journal of the Royal Statistical Society. Series B (Methodological), 36 (1):
99-102(1974)
Abstract
This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V<sup>2</sup> is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.
%0 Journal Article
%1 dfandrews1974scale
%A D. F. Andrews, C. L. Mallows
%D 1974
%I Royal Statistical Society
%J Journal of the Royal Statistical Society. Series B (Methodological)
%K Gaussian_distributions elliptically_contoured_distributions normal_scale_mixtures stable_distributions statistics
%N 1
%P 99-102
%T Scale Mixtures of Normal Distributions
%U http://www.jstor.org/stable/2984774
%V 36
%X This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V<sup>2</sup> is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.
@article{dfandrews1974scale,
abstract = {This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V<sup>2</sup> is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.},
added-at = {2016-06-30T05:24:02.000+0200},
author = {D. F. Andrews, C. L. Mallows},
biburl = {https://www.bibsonomy.org/bibtex/2bf5d23696072766dde074695ff921823/peter.ralph},
interhash = {9ffa7bef53e1aa597463510f26fbde48},
intrahash = {bf5d23696072766dde074695ff921823},
issn = {00359246},
journal = {Journal of the Royal Statistical Society. Series B (Methodological)},
keywords = {Gaussian_distributions elliptically_contoured_distributions normal_scale_mixtures stable_distributions statistics},
number = 1,
pages = {99-102},
publisher = {Royal Statistical Society},
timestamp = {2016-06-30T05:24:02.000+0200},
title = {Scale Mixtures of Normal Distributions},
url = {http://www.jstor.org/stable/2984774},
volume = 36,
year = 1974
}