Tests for and against Trends Among Poisson Intensities.
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 chi-bar-squared 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1982
- Accession Number
- ADA131212
Entities
People
- F. T. Wright
- Rhonda Magel