On a characteristic property of distributions related to the Laplace

M. C. Jones

doi:10.37920/sasj.2019.53.1.3

M. C. Jones School of Mathematics and Statistics, The Open University, Milton Keynes, United Kingdom

DOI: https://doi.org/10.37920/sasj.2019.53.1.3

Keywords: Asymmetric Laplace distribution, Double Pareto distribution, Ratios of random variables

Abstract

It is shown that the asymmetric Laplace distribution uniquely arises as the distribution of both a difference between independent positive random variables and of a random choice between those random variables, one of them having been given a negative sign. Related results on the positive half-line are also given.

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