On the discrete analogues of continuous distributions |
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| Institution: | 1. Department of Mathematics & Statistics, Austin Peay State University, Clarksville, TN 37044, United States;2. Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, United States;1. Production Department, São Paulo State University (UNESP), Guaratinguetá, SP, Brazil;2. Chair of Statistics, Military Academy of Agulhas Negras (AMAN), Resende, RJ, Brazil;1. Grupo Física-Matemática, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal;2. Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal;3. Mathematical Institute, University of Oxford, 24-29 St Giles'', Oxford OX1 3LB, England, United Kingdom;1. Infinio Systems, Inc., United States;2. IBM T. J. Watson Research Center, United States |
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| Abstract: | In this paper, a new method is proposed for generating discrete distributions. A special class of the distributions, namely, the T-geometric family contains the discrete analogues of continuous distributions. Some general properties of the T-geometric family of distributions are obtained. A member of the T-geometric family, namely, the exponentiated-exponential–geometric distribution is defined and studied. Various properties of the exponentiated-exponential–geometric distribution such as the unimodality, the moments and the probability generating function are discussed. The method of maximum likelihood estimation is proposed for estimating the model parameters. Three real data sets are used to illustrate the applications of the exponentiated-exponential–geometric distribution. |
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