A Discrete Distribution Arising as a Solution of a Linear Difference Equation: Extension of the Non Central Negative Binomial Distribution |
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| Authors: | S H Ong K Shimizu |
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| Institution: | 1. Institute of Mathematical Sciences, University of Malaya , Kuala Lumpur, Malaysia ngsh@um.edu.my;3. Department of Mathematics , Keio University , Yokohama, Japan |
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| Abstract: | This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered. |
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| Keywords: | Goodness of fit Index of dispersion Mixed compound generalized distributions Mixed Poisson and birth–death with immigration processes Parameter estimation Weighted distribution |
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