On the Bell distribution and its associated regression model for count data

Castellares, Fredy; Ferrari, Silvia L. P.; Lemonte, Artur J.

doi:10.1016/j.apm.2017.12.014

Cited by 62 publications

(49 citation statements)

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“…Two practical examples are provided to show that the Bin-PL regression model works very well, and this is confirmed by comparing it with the classical Poisson, uniform-Poisson (UP) [7] and Bell [4] models.…”

Section: Introductionmentioning

confidence: 72%

The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression

Chesneau¹

2022

CMR

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Section: Introductionmentioning

confidence: 72%

The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression

Chesneau¹

2022

CMR

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“…Some Bell numbers are listed as follows. For the convenience of the reader, we introduce the following definition and properties of the Bell distribution described in Castellares et al (2018) [16]:…”

Section: The Bell Distributionmentioning

confidence: 99%

“…where Y n has zero-truncated Poisson distribution with parameter θ, and N ∼ Poisson(e θ − 1). See Castellares et al (2018) [16] for more properties.…”

Section: The Bell Distributionmentioning

confidence: 99%

“…Although several models have been proposed in recent years, most of the considered distributions are based on some generalizations of the Poisson distribution and have more than one parameter, such as the zero-inflated Poisson, compound Poisson, double Poisson, and generalized Poisson distributions. Here we use a relatively simple distribution introduced by Castellares et al (2018)[16] for the innovations, i.e., the Bell distribution. It has the advantages of having only one parameter, belonging to the exponential family, having a simple probability mass function, and having infinite divisibility.…”

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confidence: 99%

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A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Huang¹,

Zhu²

2021

Entropy

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A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule–Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates’ performances. Real data examples are provided.

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“…O objetivo é propor um novo modelo para análise de dados de sobrevivência de longa duração denominado Bell-Inversa Gaussiana com proporção de cura (BIGcr). Assumimos que há diferentes mecanismos de ativação com causas latentes para o evento de interesse, cujo o número dessas causas é modelado por uma distribuição Bell (CASTELLARES;FERRARI;LEMONTE, 2018) e o tempo até a ocorrência do evento de interesse segue uma distribuição Inversa Gaussiana (IG).…”

Section: Capítulo 1 Introduçãounclassified

Um novo modelo de sobrevivência Bell-Inversa Gaussiana com fração de cura

Carregari¹

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Neste trabalho propomos um novo modelo de sobrevivência denominado Bell-Inversa Gaussiana com fração de cura. Consideramos diferentes esquemas de ativação em que o número de fatores M tem a distribuição Bell e o tempo de ocorrência de um evento segue o modelo Inversa Gaussiana. Os parâmetros são estimados pelos métodos clássico e Bayesiano. Em um estudo de simulação, investigamos as médias das estimativas, os vieses, os erros quadráticos médios e as probabilidades de cobertura nos diferentes esquemas de ativação. Com o objetivo de detectar possíveis observações influentes ou extremas que podem causar distorções nos resultados da análise, utilizamos o método Bayesiano de análise de influência de deleção de casos baseado na divergência ψ. Por fim, mostramos a aplicabilidade do modelo proposto a um conjunto de dados reais.

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On the Bell distribution and its associated regression model for count data

Cited by 62 publications

References 5 publications

The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression

The Binomial-Discrete Poisson-Lindley Model: Modeling and Applications to Count Regression

A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Um novo modelo de sobrevivência Bell-Inversa Gaussiana com fração de cura

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