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Journal ArticleDOI

The discrete Lindley distribution: properties and applications

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TLDR
In this article, a new probability mass function is introduced by discretizing the continuous failure model of the Lindley distribution, which is suitable to be applied in the collective risk model when both number of claims and size of a single claim are implemented into the model.
Abstract
Modelling count data is one of the most important issues in statistical research. In this paper, a new probability mass function is introduced by discretizing the continuous failure model of the Lindley distribution. The model obtained is over-dispersed and competitive with the Poisson distribution to fit automobile claim frequency data. After revising some of its properties a compound discrete Lindley distribution is obtained in closed form. This model is suitable to be applied in the collective risk model when both number of claims and size of a single claim are implemented into the model. The new compound distribution fades away to zero much more slowly than the classical compound Poisson distribution, being therefore suitable for modelling extreme data.

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Citations
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A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries.

TL;DR: In this article , a discrete mixture model is proposed for modeling extreme and outliers' observations, where the base distribution can be expressed as a mixture of gamma and Lindley models.
Journal Article

On estimation of the probability mass function and the cumulative distribution function of a natural discrete one parameter polynomial exponential distribution

TL;DR: In this paper, a new natural discrete analog of the one parameter polynomial exponential (OPPE) distribution as a mixture of a number of negative binomial distributions has been proposed and is called as a natural discrete one parameter POINTE distribution.
Journal ArticleDOI

Discrete Extension of Poisson Distribution for Overdispersed Count Data: Theory and Applications

TL;DR: In this paper , a new one-parameter discrete probability distribution is introduced for overdispersed count data based on a combining approach, and the important statistical properties can be expressed in closed forms including factorial moments, moment generating function, dispersion index, coefficient of variation and coefficient of skewness.

On Type-II Hybrid Censored Lindley

TL;DR: In this paper, the authors deal with the inferential study of Lindley distribution when the data are type-II hybrid censored and derive the maximum likelihood estimate of the parameter with its standard error.
References
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Book

Theory of point estimation

TL;DR: In this paper, the authors present an approach for estimating the average risk of a risk-optimal risk maximization algorithm for a set of risk-maximization objectives, including maximalaxity and admissibility.
Book

Loss Models: From Data to Decisions

TL;DR: In this paper, the authors present an inventory of continuous and discrete time-ruiner models for complete and modified data sets, as well as a comprehensive inventory of discrete and continuous distributions for complete data sets.
Journal ArticleDOI

A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families

TL;DR: In this article, a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used twoparameter families of life distributions as the Weibull, gamma and lognormal distributions.
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