Scale Mixtures of Normal Distributions

Abstract

Summary 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 2 is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.