Journal ArticleDOI
The discrete Lindley distribution: properties and applications
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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 Article
On strength reliability for lindley distributed stress
M. J. S. Khan,Surinder K +1 more
TL;DR: In this article, the problem of strength of a manufactured item facing Lindley distributed stress and power function distribution as strength was considered from a different perspective, i.e. by finding the relationship among the parameters of these distributions.
Journal ArticleDOI
A Discrete Linear-Exponential Model: Synthesis and Analysis with Inference to Model Extreme Count Data
TL;DR: In this paper , a novel probability discrete model is introduced for modeling overdispersed count data, which can be used to discuss right-skewed data with heavy tails and its hazard rate function can be utilized to model the phenomena with a monotonically increasing failure rate shape.
Posted Content
Bivariate Discrete Exponentiated Weibull Distribution: Properties and Applications
M. El Morshedy,A. A. Khalil +1 more
TL;DR: In this article, a new bivariate discrete distribution is introduced which called Bivariate Discrete Exponentiated Weibull (BDEW) distribution, and several of its mathematical statistical properties are derived such as the joint cumulative distribution function, the joint joint hazard rate function, probability mass function, joint moment generating function, mathematical expectation and reliability function for stress-strength model.
Proceedings ArticleDOI
Discrete Lindley distribution
TL;DR: Characteristics of Discrete Lindley distribution that are obtained are unimodal, right skew, high fluidity and overdispersion, which is appropriate to be used as an alternative to Poisson distribution in modeling overdispersed count data.
Book ChapterDOI
Modeling Correlated Counts in Reliability Engineering
TL;DR: This chapter reviews the problem of modeling correlated count data and focuses on the copula approach, illustrating its advantages, but also possible limitations and issues arising in the discrete context if compared to the continuous case.
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.
Journal ArticleDOI
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.
Journal ArticleDOI