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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Journal ArticleDOI
Exponential-modified discrete Lindley distribution.
TL;DR: The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also parameters of this new lifetime distribution are estimated by using moments, maximum likelihood and EM-algorithm.
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Size-biased discrete two parameter Poisson-Lindley Distribution for modeling and waiting survival times data
TL;DR: In this paper, the authors introduced the notion of Size-biased discrete two-parameter Poisson-Lindley (SBDTPPL) distribution and derived its p.m.f., some of its properties and the expressions for raw and central moments, coefficients of skewness and kurtosis.
A Discrete Analogue of Teissier Distribution: Properties and Classical Estimation with Application to Count Data
TL;DR: In this article , a discrete Teissier distribution with a single parameter is proposed, which offers a high degree of fitting flexibility as it is capable of modelling equi-, over-, and under-dispersed, positive and negative skewed, and increasing failure rate datasets.
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A generalization of sujatha distribution and its applications with real lifetime data
TL;DR: In this article, a two-parameter generalization of Sujatha distribution (AGSD) is proposed, which includes Lindley distribution as particular cases, and the maximum likelihood estimation method has been discussed for estimating its parameters, including its shape for varying values of parameters, moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress strength reliability have been discussed.
Journal ArticleDOI
The Marshall-Olkin Modified Lindley Distribution: Properties and Applications
TL;DR: In this article, a new Marshall-Olkin distribution by using a modification of the Lindley distribution is proposed, and the parameters of the new model are estimated using the maximum likelihood method.
References
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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.
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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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