A new generalized Poisson-Lindley distribution is obtained by compounding Poisson distribution with a two parameter generalised Lindley distribution. The new distribution is shown to be unimodal and over-dispersed. This distribution has a tendency to accommodate right tail, and for particular values of parameter, the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, moments etc. are derived. Knowledge about the parameters is obtained through method of moments, maximum likelihood method and EM algorithm. Moreover, an actuarial application to collective risk model is shown by considering the proposed distribution as primary distribution and exponential and Erlang as secondary distributions. The model is applied to real data sets and found to perform better than other competing models.
In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments, entropy, and limiting distribution of extreme order statistics are established . Inference for a random sample from the proposed distribution is investigated and maximum likelihood estimation method is used for estimating parameters of this distribution. The applicability of the proposed distribution is shown through real data sets.
In this paper, 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 distribution as mixing distribution. Some distributional properties like unimodality, moments, over-dispersion, Taylor series expansion of proposed model are studied. Estimation of the parameters using method of moments, method of moments and proportion and maximum likelihood estimation along with data fitting experiment to show its advantage over some existing distribution. Further, an actuarial applications in context of aggregate claim distribution is discussed. Finally, we discuss a count regression model based on proposed distribution and its usefulness over some well established model.
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