
Accession Number : ADA131212
Title : Tests for and against Trends Among Poisson Intensities.
Descriptive Note : Interim rept.,
Corporate Author : MISSOURI UNIVROLLA
Personal Author(s) : Magel,Rhonda ; Wright,F T
PDF Url : ADA131212
Report Date : Nov 1982
Pagination or Media Count : 16
Abstract : Suppose one observes independent Poisson processes with unknown intensities lambda sub: i = 1,2,...,k, and that apriori it is believed that these intensities satisfy a known ordering. For preliminary analysis, it might be desirable to test for homogeneity among the intensities and, of course, one would want a test that utilizes the information in the ordering. Let t sub i denote the length of time for which the ith process was observed. The case in which the t sub i are equal has been studied in the literature. We develop the conditional likelihood ratio test for arbitrary t sub i are equal has been studied in the literature. We develop the conditional likelihood ratio test for arbitrary t sub i. This test is equivalent to the unconditional likelihood ratio test, but leads to an interesting multinomial testing situation, ie. testing for homogeneity of p sub i/t sub i versus a trend among the p sub i/t sub i, where the p sub i are the cell probabilities. If the number of trials in the multinomial setting, or the total number of occurrences in the Poisson processes, is large, then the test statistic has an approximate chibarsquared distribution which has been studied in the literature. Results of a Monte Carlo study comparing this test with the maximin test developed by Y. J. Lee are discussed. Similar results are also obtained for testing the null hypothesis that the intensities satisfy the prescribed ordering. (Author)
Descriptors : *Statistical tests, *Poisson density functions, *Poisson ratio, Monte Carlo method, Maximum likelihood estimation, Comparison, Hypotheses, Homogeneity, Intensity, Probability
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE