On estimation of the Poisson parameter in zero-modified Poisson models.
type: Item
instance of: scholarly article
title: On estimation of the Poisson parameter in zero-modified Poisson models.
zbMATH Open document ID: 1046.62085
DOI: 10.1016/S0167-9473(99)00111-5
published in: Computational Statistics and Data Analysis
publication date: 2000-10-26T00:00:00Z
review text: For count data, typically a Poisson model is assumed. However, it has been observed in various applications that this model does not fit, because of too few or too many zeros in the data. For the latter case the zero-inflated Poisson (regression) model has been proposed. In situations where, for certain reasons, no zeros at all can be observed, the zero-truncated Poisson (regression) model is appropriate. This paper provides an EM algorithm for ML estimation of the latter model by standard software for Poisson regression. It is shown, that this algorithm can be used also to estimate the Poisson parameters of zero-inflated, zero-deflated, and standard Poisson models, when the zero observations are ignored. If nothing is known about the kind of zero modification, the respective estimates are fully efficient. Situations are described, in which the loss of efficiency is small although knowledge of the kind of zero modification is available. In a second step, the respective estimates of the Poisson parameter can be used to analyze the kind of zero modification and to estimate the zero modification parameter.
Mathematics Subject Classification ID: 62M09
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 62M05
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1521874
zbMATH Keywords: zero-modified Poisson model
zbMATH Keywords: zero-truncated Poisson model
zbMATH Keywords: zero-inflated Poisson model
zbMATH Keywords: zero-deflated Poisson model
author: Ekkehart Dietz
author: Dankmar Böhning
MaRDI profile type: Publication
cites work: An Extension of a Truncated Poisson Distribution
cites work: Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space
cites work: Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing
cites work: On inference for a mixture of a poisson and a degenerate distribution
full work available at URL: s0167-9473(99)00111-5
OpenAlex ID: W1975095546
Wikidata QID: Q127526457
description: scientific article; zbMATH DE number 1521874