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Maximum Likelihood Estimation of Exponential Polynomial Rate for Poisson Data
Author(s) -
Mathers C. D.
Publication year - 1984
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710260106
Subject(s) - mathematics , exponential function , statistics , exponential family , likelihood function , quasi likelihood , poisson distribution , monte carlo method , likelihood ratio test , quadratic function , quadratic equation , maximum likelihood , exponential distribution , count data , mathematical analysis , geometry
Abstract The heterogeneous Poisson process with discretized exponential quadratic rate function is considered. Maximum likelihood estimates of the parameters of the rate function are derived for the case when the data consists of numbers of occurrences in consecutive equal time periods. A likelihood ratio test of the null hypothesis of exponential quadratic rate is presented. Its power against exponential linear rate functions is estimated using Monte Carlo simulation. The maximum likelihood method is compared with a log‐linear least squares techniques. An application of the technique to the analysis of mortality rates due to congenital malformations is presented.