Article ID Journal Published Year Pages File Type
1149065 Journal of Statistical Planning and Inference 2006 13 Pages PDF
Abstract

Following Kemp (J. Statist. Plann. Inference 63 (1997) 223) who defined a discrete analogue of the normal distribution, we derive a discrete version of the Laplace (double exponential) distribution. In contrast with the discrete normal case, here closed-form expressions are available for the probability density function, the distribution function, the characteristic function, the mean, and the variance. We show that this discrete distribution on integers shares many properties of the classical Laplace distribution on the real line, including unimodality, infinite divisibility, closure properties with respect to geometric compounding, and a maximum entropy property. We also discuss statistical issues of estimation under the discrete Laplace model.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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