A discrete analogue of the Laplace distribution |
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| Institution: | 1. Department of Biostatistics, University of Alabama, Birmingham, AL 35294, USA;2. Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA;1. University of Wisconsin–Madison, Mathematics Department, 480 Lincoln Dr., Madison, WI, 53706, USA;2. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047 Moscow, Russia;1. Departamento de Matemática, UFOP, 35400-000, Ouro Preto, MG, Brazil;2. Departamento de Matemática, UFMG, 30161-970, Belo Horizonte, MG, Brazil;1. School of Science, Beijing University of Posts and Telecommunications, Beijing, China;2. Advanced Institute of Natural Sciences, Beijing Normal University, Zhuhai, China;3. BNU-HKBU United International College, Zhuhai, China;4. Department of Computer Science and Engineering, University of Nebraska-Lincoln, NE, USA |
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| 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. |
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