Journal of Statistical Planning and Inference 136 (2006) 1090 – 1102 www.elsevier.com/locate/jspi A discrete analogue of the Laplace distribution  Seidu Inusah a , Tomasz J. Kozubowski b, ∗ a Department of Biostatistics, University of Alabama, Birmingham, AL 35294, USA b Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA Received 16 September 2003; accepted 18 August 2004 Available online 7 October 2004 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. © 2004 Elsevier B.V.All rights reserved. MSC: 60E05; 60E07; 62E10; 62F10; 62F12 Keywords: Discrete normal distribution; Double exponential distribution; Exponential distribution; Geometric infinite divisibility; Infinite divisibility; Laplace distribution; Maximum entropy property; Maximum likelihood estimation 1. Introduction The classical normal distribution is characterized by the property of having maximum (Shannon) entropy among all continuous distributions supported on R with specified second moment (see, e.g., Lisman and van Zuylen, 1972), or with specified mean and variance  Research was partially supported by NSF Grant DMS-0139927. ∗ Corresponding author. Tel.: +1 7757846643; fax: +1 7757846378. E-mail address: tkozubow@unr.edu (T.J. Kozubowski). 0378-3758/$ - see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jspi.2004.08.014