%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 1/2V² 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 1/2V² 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 }