A new count model generated from mixed Poisson transmuted exponential family with an application to health care data |
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Authors: | Deepesh Bhati Pooja Kumawat E Gómez–Déniz |
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Institution: | 1. Department of Statistics, Central University of Rajasthan, Ajmer, Rajasthan, India;2. Department of Quantitative Methods in Economics and TiDES Institute. University of Las Palmas de Gran Canaria, Spain |
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Abstract: | In this article, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential as mixing distribution. Distributional properties like unimodality, moments, over-dispersion, infinite divisibility are studied. Three methods viz. Method of moment, Method of moment and proportion, and Maximum-likelihood method are used for parameter estimation. Further, an actuarial application in context of aggregate claim distribution is presented. Finally, to show the applicability and superiority of proposed model, we discuss count data and count regression modeling and compare with some well established models. |
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Keywords: | Count regression health care data mixed Poisson distribution over-dispersion transmuted exponential family |
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