Binomial-Discrete Lindley Distribution

Kuş, Çoşkun; Akdoğan, Yunus; Asgharzadeh, Akbar; Kınacı, İsmail; Karakaya, Kadir

doi:10.31801/cfsuasmas.424228

Cited by 18 publications

(10 citation statements)

References 17 publications

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“…Khan [10] proposed the proportions estimators (PEs) to estimate the unknown parameters of discrete Weibull distribution. The same idea is also used in Akdoğan et al [1] and Kuş et al [11] and can be applied to estimate the CosPois parameters. Let X 1 , X 2 , .…”

Section: Methods Of Proportionsmentioning

confidence: 99%

The Cos-Poisson model with a novel count regression analysis

Bakouch

Chesneau

Karakaya

et al. 2021

Hacettepe Journal of Mathematics and Statistics

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In this paper, we propose a new generalization of the Poisson distribution by using the concept of the weighted distribution; a trigonometric weight with the cosine function is used. We derive some distributional properties of the new distribution, such as the cumulative distribution function, moment generating function, factorial moments, and index of dispersion. Then, the related model is considered for modeling purposes, with estimation of the model parameters performed via several methods. Zero-inflated count regression analysis is introduced by using the new distribution. Finally, we provide two applications of the obtained results on practical data sets.

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Section: Methods Of Proportionsmentioning

confidence: 99%

The Cos-Poisson model with a novel count regression analysis

Bakouch

Chesneau

Karakaya

et al. 2021

Hacettepe Journal of Mathematics and Statistics

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“…In recent studies, new discrete models have been constructed by compounding two discrete distributions. For example, Déniz [11] defined the uniform Poisson, Akdogan et al [12] proposed the uniform geometric, and Kuş et al [13] introduced the binomial discrete Lindley.…”

Section: Introductionmentioning

confidence: 99%

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

et al. 2021

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We propose a new asymmetric discrete model by combining the uniform and Poisson–Ailamujia distributions using the binomial decay transformation method. The distribution, named the uniform Poisson–Ailamujia, due to its flexibility is a good alternative to the well-known Poisson and geometric distributions for real data applications in public health, biology, sociology, medicine, and agriculture. Its main statistical properties are studied, including the cumulative and hazard rate functions, moments, and entropy. The new distribution is considered to be suitable for modeling purposes; its parameter is estimated by eight classical methods. Three applications to biological data are presented herein.

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“…The negative binomial

distribution (that may arise as a

mixture model by using a gamma distribution for the continuous part) is undoubtedly the most popular alternative to model extra-

variability. There is extensive literature regarding other discrete mixed distributions that can accommodate different levels of overdispersion, for example, the Poisson–Lindley [ 2 ], the Poisson–lognormal [ 3 ], the Poisson–inverse Gaussian [ 4 ], the negative binomial–Lindley [ 5 ], the Poisson–Janardan [ 6 ], the two-parameter Poisson–Lindley [ 7 ], the Poisson–Amarendra [ 8 ], the Poisson–Shanker [ 9 ], the Poisson–Sujatha

[ 10 ], the quasi-Poisson–Lindley [ 11 ], the weighted negative binomial–Lindley [ 12 ] the Poisson-weighted Lindley [ 13 ], the binomial-discrete Lindley [ 14 ], and the two-parameter Poisson–Sujatha [ 15 ], among many others.…”

Section: Introductionmentioning

confidence: 99%

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Bertoli

Conceição

Andrade

et al. 2021

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Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper’s primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson–Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators’ empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

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Binomial-Discrete Lindley Distribution

Cited by 18 publications

References 17 publications

The Cos-Poisson model with a novel count regression analysis

The Cos-Poisson model with a novel count regression analysis

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

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