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Poisson Generated Family of Distributions: A Review

Sandeep Kumar Maurya () and Saralees Nadarajah ()
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Sandeep Kumar Maurya: Central University of South Bihar
Saralees Nadarajah: University of Manchester

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 12, 484-540

Abstract: Abstract The present article represents a survey on Poisson generated family of distributions. Based on this family of distribution, several transformations and distributions have been proposed. Out of which, some of them are proposed by referencing it, and some are independent. The family can be proposed by using the compounding concept of zero truncated Poisson distribution with any other model or family of distributions. Here, we provide a complete survey on this family of distributions and list the contributory related research works. We also address 12 power series distributions, 77 distributions based on the Poisson family of distribution, and 23 distributions, based on different ten transformation methods based on this family of distribution. These numbers show the importance of the Poisson family of distribution.

Keywords: Lifetime models; Poisson distribution; Power series distribution; Compounding of distribution function; Transformation method; Primary: 60-02, 60E05; Secondary: 62F10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00237-8

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Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00237-8