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.read more
Citations
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A Suitable Discrete Distribution for Modelling Automobile Claim Frequencies
TL;DR: In this article, a new discrete distribution, depending on two parameters, is introduced, with the discrete Lindley acting as the mixed and the Beta prime as the mixing distribution, and the distribution obtained is shown to be unimodal and overdispersed.
Journal ArticleDOI
Binominal Mixture Lindley Distribution: Properties and Applications
TL;DR: The binomial mixture Lindley distribution (BMLD) as mentioned in this paper is a generalized mixture distribution, which is obtained by mixing binomial probabilities with gamma distribution, and the density function of this distribution is obtained.
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Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process
TL;DR: In this paper, a discrete version of the pseudo-Lindley distribution, called the discrete Pseudo Lindley (DPsL) distribution, is proposed, and its empirical importance is proved through three real datasets.
Journal ArticleDOI
Odoma Distribution and Its Application
TL;DR: In this article, a new continuous one parameter lifetime distribution is proposed and its mathematical properties such as moments, order statistics, entropy, survival function, hazard rate function and mean residual life function are derived.
Journal Article
The Compound DGL/Erlang Distribution in the Collective Risk Model // La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo
TL;DR: In this paper, the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribution, is considered, and analytical expressions for the aggregate claim size distribution in general insurance are derived.
References
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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.
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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.
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A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families
Albert W. Marshall,Ingram Olkin +1 more
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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