Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution
type: Item
instance of: scholarly article
title: Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution
zbMATH Open document ID: 0564.62037
author: Kazutomo Kawamura
published in: Kodai Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: To estimate the parameter vector \(\lambda\) of the bivariate Poisson distribution we would like to calculate the maximum likelihood estimator (MLE) \({\hat \lambda}\). This MLE \({\hat \lambda}\) has not a simple expression as \(\bar X,\) \(S^ 2,..\). etc. We only have information about MLE \({\hat \lambda}\) by normal equations and its variation forms. \textit{P. Holgate} [Biometrika 51, 241-245 (1964; Zbl 0133.118)] shows the asymptotic property of MLE \({\hat \lambda}\). In this paper we present a calculating method of MLE \({\hat \lambda}\). The method is constructed by direct calculation of likelihood function and by a searching routine of MLE \({\hat \lambda}\) which maximizes the function value. A sequence of random numbers coming from a bivariate Poisson distribution P(\(\lambda)\) is given. The change of the value of the likelihood function varying parameter \(\lambda\) in our rule is calculated and the performance of the searching routine is discussed in detail. In the last part of this paper a numerical interpretation of our routine is shown.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 62-04
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 3899960
zbMATH Keywords: bivariate Poisson distribution
zbMATH Keywords: maximum likelihood estimator
zbMATH Keywords: direct calculation of likelihood function
zbMATH Keywords: searching routine of MLE
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138036908
OpenAlex ID: W1965367474
cites work: The structure of bivariate Poisson distribution
cites work: Poisson approximation for sums of independent bivariate Bernoulli vectors
cites work: Q4043971
cites work: Estimation for the bivariate Poisson distribution
DOI: 10.2996/KMJ/1138036908
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description: scientific article; zbMATH DE number 3899960