Weighted Negative Binomial Poisson-Lindley Distribution with Actuarial Applications

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.

Construction, Characterization, Estimation and Performance Analysis of Selection Generalized Nakagami Distributions with Environmental Applications

“…Also, Havrda and Charvat [15] introduced −entropy class as follows: where is a non-stochastic constant, by using (15) and (7) and after some elementary algebra, we have:…”

“…Let X 1 , X 2 , ..., X N be random variables that are i.i.d. according to (7) and Θ = ( i, j, , , Ω ) T . The log-likelihood function of the independent multivariate generalized weighted of the NA distribution based on X 1 , X 2 , ..., X N is given by…”

“…In this article, we pay attention to a selection model from the NA distribution. Selection distributions have been considered extensively by many authors; for a best survey of estimation method discussions and applications, see Heckman [2], Copas and Li [3], Arrellano-Valle et al [4], Signer et al [5], Balakrishnan et al [6], Zamani et al [7] and Arashi et al [8] and more recently. The organization of this paper is as follows: In Section 2, we present definition and some representations of this model.…”