Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

Hossein Zamani; Noriszura Ismail; Marzieh Shekari

doi:10.20944/preprints201805.0026.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 30 April 2018 / Approved: 2 May 2018 / Online: 2 May 2018 (11:47:51 CEST)

This study introduces a new discrete distribution which is a weighted version of Poisson-Lindley distribution. The weighted distribution is obtained using the negative binomial weight function and can be fitted to count data with over-dispersion. The p.m.f., p.g.f. and simulation procedure of the new weighted distribution, namely weighted negative binomial Poisson-Lindley (WNBPL), are provided. The maximum likelihood method for parameter estimation is also presented. The WNBPL distribution is fitted to several insurance datasets, and is compared to the Poisson and negative binomial distributions in terms of several statistical tests.

weighted distribution; Poisson-Lindley distribution; discrete distribution; weighted negative binomial Poisson-Lindley distribution

Computer Science and Mathematics, Probability and Statistics

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Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

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