Connections of the Poisson weight function to overdispersion and underdispersion

Kokonendji, Célestin C.; Mizère, Dominique; Balakrishnan, N.

doi:10.1016/j.jspi.2007.05.028

Cited by 83 publications

(65 citation statements)

References 16 publications

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“…In particular, viewing the COM-Poisson distribution as a weighted Poisson distribution (Kokonendji et al, 2008) allows us to propose a cure rate model which includes some of the well-known cure rate models in the literature due to Berkson and Gage (1952), Yakovlev and Tsodikov (1996) and Yin and Ibrahim (2005). The COM-Poisson distribution, introduced by Conway and Maxwell (1961), was revived recently by Shmueli et al (2005).…”

Section: Discussionmentioning

confidence: 99%

COM–Poisson cure rate survival models and an application to a cutaneous melanoma data

Rodrigues

Castro

Cancho

et al. 2009

Journal of Statistical Planning and Inference

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101

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Section: Discussionmentioning

confidence: 99%

COM–Poisson cure rate survival models and an application to a cutaneous melanoma data

Rodrigues

Castro

Cancho

et al. 2009

Journal of Statistical Planning and Inference

Self Cite

129

101

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“…When φ = 0 and η < 1, the COM-Poisson reduces to the geometric distribution with parameter 1 − η, and is undefined for η ≥ 1. Shmueli et al [10] and Kokonendji et al [21] discussed various statistical and probabilistic properties of Equation (2), including sufficient statistics, three methods of estimation and extensions. Recently, Nadarajah [14] derived for the first time exact and explicit expressions for its moments and the cumulative distribution function for the case of over-dispersion.…”

Section: The Modelmentioning

confidence: 99%

The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors

Cancho¹,

Ortega

Barriga

et al. 2011

Journal of Statistical Computation and Simulation

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In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

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“…Kokonendji et al, 2008), ensuite nous procéderonsà la décomposition de la loi de Poisson pondérée en une combinaison convexe des lois duales. Deux exemples d'illustration seront donnés selon que les lois f j soient duales ponctuelles ou duales en moyenne.…”

Section: Introductionunclassified

Decomposition d'une loi de poisson ponderee en une combinaison convexe de lois duales

Mizère¹,

Louzayadio²,

Bidounga³

et al. 2013

afst

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Abstract. The probability distribution of a set of observation is most often defined as a convex combination of probability laws. To highlight this mixture of the laws, MCMC (Monte Carlo Markov Chain) which is an algorithm that generates a stationary Markov chain is often used; laws being considered as normal laws. In this paper, the observations are positive integer, so it is assumed that the mixture law is a Poisson weighted law and Blending laws are dual. The purpose of this work is to determine the dual laws by simple algebraic properties.Résumé. La loi de distribution d'un ensemble d'observation est le plus souvent définie comme une combinaison convexe de plusieurs lois de probabilités. Pour mettre enévidence ce mélange de lois on utilise souvent la méthode MCMC (Monte Carlo par Chaîne de Markov) qui est un algorithme qui génère une chaîne de Markov stationnaire; les loisétant considérées comme des lois normales. Dans le présent papier, les observations sont entières positives; on suppose donc que la loi mélange est une loi de Poisson pondérée et les lois mélangeantes sont duales . L'objet de ce travail est de pouvoir déterminer ces lois duales par des propriétés algébriques simples.

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Connections of the Poisson weight function to overdispersion and underdispersion

Cited by 83 publications

References 16 publications

COM–Poisson cure rate survival models and an application to a cutaneous melanoma data

COM–Poisson cure rate survival models and an application to a cutaneous melanoma data

The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors

Decomposition d'une loi de poisson ponderee en une combinaison convexe de lois duales

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