Journal ArticleDOI
The generalized poisson distribution when the sample mean is larger than the sample variance
P. C. Consul,Mohamed Shoukri +1 more
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In this article, the generalized Poisson distribution (GPD) was used to fit data arising in various situations and in many fields, and the truncation error for most cases is negligible and that the model can be used without any correction for truncation.Abstract:
The generalized Poisson distribution (GPD), containing two parameters and studied by many researchers, was found to fit data arising in various situations and in many fields. It is generally assumed that both parameters (θ,λ) are non-negative, and hence the distribution will have a variance larger than the mean. However, it appears that the distribution, as a descriptive model, fits many data for negative values of λ, which implies that the mean must be greater than the variance. Thetruncation of the GPD, proposed to remedy the deficiency in the model in this case, is investigated on the basis of the error analysis on the computer and it is suggested that the truncation error for most of the cases is negligible and that the model can be used without any correction for truncation.read more
Citations
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Journal ArticleDOI
Generalized Poisson regression model
P.C. Consul,Felix Famoye +1 more
TL;DR: In this paper, a generalized Poisson regression (GPR) model is proposed to predict a response variable affected by one or more covariates, which is suitable for both types of dispersions.
Journal ArticleDOI
Restricted generalized poisson regression model
TL;DR: In this article, restricted generalized poisson regression model is used to predict a response variable affected by one or more explanatory variables. But the model is not suitable for counting over-dispersed and under-disparished count data.
Proceedings ArticleDOI
A branching process approximation to cascading load-dependent system failure
TL;DR: A probabilistic model of loading dependent cascading failure is studied by approximating the propagation of failures as a Poisson branching process to introduce a saturating form of the generalized Poisson distribution so that supercritical systems with a high probability of total failure can be considered.
Journal ArticleDOI
Modeling and Simulation of Count Data
TL;DR: This tutorial presents the basics and diagnostics of count modeling and simulation in the context of pharmacometrics, and consideration is given to overdispersion, underdisPersion, autocorrelation, and inhomogeneity.
Journal ArticleDOI
On the bivariate generalized poisson distribution
TL;DR: In this paper, a comparative study with the bivariate generalized Poisson distribution and with two bivariate mixed Poisson distributions has been carried out, based on data concerning natural events insurance in the USA and third party liability automobile insurance in France.
References
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Journal ArticleDOI
An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents
Major Greenwood,G. Udny Yule +1 more
Journal ArticleDOI
A Generalization of the Poisson Distribution
P.C. Consul,G. C. Jain +1 more
TL;DR: In this paper, a generalization of the Poisson distribution with two parameters λ1 and λ2 is obtained as a limiting form of the generalized negative binomial distribution, where the variance of the distribution is greater than, equal to or smaller than the mean according as λ 2 is positive, zero or negative.