Preprint Article Version 1 This version is not peer-reviewed

Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

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

How to cite: Zamani, H.; Ismail, N.; Shekari, M. Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications. Preprints 2018, 2018050026 (doi: 10.20944/preprints201805.0026.v1). Zamani, H.; Ismail, N.; Shekari, M. Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications. Preprints 2018, 2018050026 (doi: 10.20944/preprints201805.0026.v1).

Abstract

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.

Subject Areas

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

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