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The Binomial-Discrete Poisson-Lindley Model:Modeling and Applications to count regression

Communications in Mathematical Research 2022年第1期38卷 28-51页

作者： Christophe Chesneau Hassan S.Bakouch Yunus Akdogan Kadir Karakaya LMNO University of Caen-NormandieCaenFrance Department of Mathematics Faculty of ScienceTanta UniversityTantaEgypt. Department of Statistics Faculty of ScienceSelcuk UniversityKonyaTurkey

On the basis of a well-established binomial structure and the socalled Poisson-Lindley distribution,a new two-parameter discrete distribution is *** properties are studied from both the theoretical and practical *** the theory,we discuss the moments,survival and hazard rate functions,mode and quantile *** statistical inference on the model parameters is investigated by the maximum likelihood,moments,proportions,least square,and weighted least square estimations.A simulation study is conducted to observe the performance of the bias and mean square error of the obtained ***,applications to two practical data sets are ***,we construct a new flexible count data regression model called the binomial-Poisson Lindley regression model with two practical examples in the medical area.

关键词： Binomial-discrete family Poisson-Lindley distribution estimation data analysis count regression

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Inference Procedures on the Generalized Poisson Distribution from Multiple Samples: Comparisons with Nonparametric Models for Analysis of Covariance (ANCOVA) of count Data

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Open Journal of Statistics 2021年第3期11卷 420-436页

作者： Maha Al-Eid Mohamed M. Shoukri Department of Biostatistics Epidemiology and Scientific Computing King Faisal Specialist Hospital and Research Center Riyadh Saudi Arabia Department of Epidemiology and Biostatistics Schulich School of Medicine and Dentistry University of Western Ontario London Ontario Canada

count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.

关键词： count regression Over Dispersion Generalized Linear Models Analysis of Covariance Generalized Additive Models

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