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Scale Mixtures of Normal Distributions

D. F. Andrews and C. L. Mallows
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 36, No. 1 (1974), pp. 99-102
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2984774
Page Count: 4
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Scale Mixtures of Normal Distributions
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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.

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