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. Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India;2. Department of Quantitative Health Sciences, Cleveland Clinic, Cleveland, OH, USA;3. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA;1. Infinio Systems, Inc., United States;2. IBM T. J. Watson Research Center, United States;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China;2. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China |
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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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