Related papers: Negative binomial models for development triangles…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
This paper proposes a new generalized linear model with the fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data with many zeros. To analyze the association of such a count variable…
In this paper, we focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type $(a,b,0)$ class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
Imputation of missing values is a strategy for handling non-responses in surveys or data loss in measurement processes, which may be more effective than ignoring them. When the variable represents a count, the literature dealing with this…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
The Chain-Ladder (CL) method remains the dominant macro-level technique for claims reserving in non-life insurance, yet its classical formulation lacks a coherent probabilistic foundation. Existing stochastic extensions-including the Mack…
A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…
In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
In this paper we present an alternative representation of the Negative Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010) which shows some advantages over the latter model. This new formulation provides a tractable…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate…
Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate…
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive…
This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that…
Negative binomial distribution is the most used distribution to model macro-parasite burden in hosts. However reliable maximum likelihood parameter estimation from data is far from trivial. No closed formula is available and numerical…