Connections of the Poisson weight function to overdispersion and underdispersion

DOI10.1016/j.jspi.2007.05.028zbMath1133.62007OpenAlexW2045722221MaRDI QIDQ2475764

Célestin C. Kokonendji, Narayanaswamy Balakrishnan, Dominique Mizere

Publication date: 11 March 2008

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2007.05.028

zbMATH Keywords

Poisson distributionweighted Poisson distributionlogconcavityCOM-Poisson distributiondual distributionlogconvexitysize-biased Poisson distribution

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Characterization and structure theory of statistical distributions (62E10)

Related Items (52)

Extended Conway-Maxwell-Poisson distribution and its properties and applications ⋮ Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family ⋮ Bridging the Gap: A Generalized Stochastic Process for Count Data ⋮ Analysis of discrete data by Conway-Maxwell Poisson distribution ⋮ Discrete dispersion models and their Tweedie asymptotics ⋮ Computing (Bivariate) Poisson Moments Using Stein–Chen Identities ⋮ The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors ⋮ Compound weighted Poisson distributions ⋮ Some characterizations and properties of COM-Poisson random variables ⋮ On some inferential issues for the destructive COM-Poisson-generalized gamma regression cure rate model ⋮ Type I multivariate zero‐inflated COM–Poisson regression model ⋮ A flexible bivariate distribution for count data expressing data dispersion ⋮ A semiparametric promotion time cure model with support vector machine ⋮ On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks ⋮ Asymptotic properties of the normalised discrete associated-kernel estimator for probability mass function ⋮ A unified view on lifetime distributions arising from selection mechanisms ⋮ Some mechanisms leading to underdispersion: Old and new proposals ⋮ Underdispersion models: Models that are “under the radar” ⋮ A Bayesian analysis of the Conway-Maxwell-Poisson cure rate model ⋮ A class of correlated weighted Poisson processes ⋮ Unnamed Item ⋮ A generalized class of form-invariant bivariate weighted distributions ⋮ Unnamed Item ⋮ Integer-valued autoregressive models for counts showing underdispersion ⋮ Relative variation indexes for multivariate continuous distributions on \([0,\infty)^k\) and extensions ⋮ A COM-Poisson type generalization of the binomial distribution and its properties and applications ⋮ Multilevel zero-inflated generalized Poisson regression modeling for dispersed correlated count data ⋮ Fisher dispersion index for multivariate count distributions: a review and a new proposal ⋮ A weighted Poisson distribution and its application to cure rate models ⋮ A class of weighted Poisson processes ⋮ An EM algorithm for the destructive COM-Poisson regression cure rate model ⋮ The COM‐Poisson model for count data: a survey of methods and applications ⋮ Reliability properties of generalized mixtures of Weibull distributions with a common shape parameter ⋮ On the Bayes estimators of the parameters of size-biased generalized power series distributions ⋮ COM-Poisson cure rate survival models and an application to cutaneous melanoma data ⋮ Semiparametric estimation for count data through weighted distributions ⋮ Discrete associated kernels method and extensions ⋮ Destructive weighted Poisson cure rate models ⋮ COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data ⋮ Flexible $M/G/1$ queueing system with state dependent service rate ⋮ Generalized mixtures of Weibull components ⋮ Relaxed Poisson cure rate models ⋮ Weighted Poisson and Semiparametric Kernel Models Applied to Parasite Growth ⋮ Discrete triangular associated kernel and bandwidth choices in semiparametric estimation for count data ⋮ Modelling counts with state-dependent zero inflation ⋮ Flexible models for overdispersed and underdispersed count data ⋮ When is the Conway-Maxwell-Poisson distribution infinitely divisible? ⋮ EM algorithm-based likelihood estimation for some cure rate models ⋮ STUDY OF ALEURODICUS DATA BY REGRESSION OF WEIGHTED POISSON DISTRIBUTIONS ZMWPD_{1}(\delta_{1}, n, \pi_{0}) AND WPD_{2}(\delta, n) ⋮ On general exponential weight functions and variation phenomenon ⋮ Asymptotic normality of the test statistics for the unified relative dispersion and relative variation indexes ⋮ Data Dispersion: Now You See It… Now You Don't

Cites Work

• Generalized Poisson models arising from Markov processes
• Weighted Poisson distributions for overdispersion and underdispersion situations
• On the monotonic properties of discrete failure rates
• Characterizations using weighted distributions
• Overdispersed and underdispersed Poisson generalizations
• A note on overdispersed exponential families
• The role of weighted distributions in stochastic modeling
• An empirical model for underdispersed count data
• Double Exponential Families and Their Use in Generalized Linear Regression
• Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families
• Analysis of Overdispersed Count Data by Mixtures of Poisson Variables and Poisson Processes
• Recursive characterization of a large family of discrete probability distributions showing extra-Poisson variation
• Univariate Discrete Distributions
• Count Data Distributions
• A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Connections of the Poisson weight function to overdispersion and underdispersion