Date of Award

Spring 2012

Degree Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics and Statistics

Supervisor

Aaron Childs

Language

English

Committee Member

Roman Viveros, Joseph Beyene

Abstract

In this thesis we study several inverse sampling procedures to test for homogeneity in a multivariate hypergeometric distribution. The procedures are finite population analogues of the procedures introduced in Panchapakesan et al. (1998) for the multinomial distribution. In order to develop some exact calculations for critical values not considered in Panchapakesan et al. we introduce some terminologies for target probabilities, transfer probabilities, potential target points, right intersection, and left union. Under the null and the alternative hypotheses, we give theorems to calculate the target and transfer probabilities, we then use these results to develop exact calculations for the critical values and powers of one of the procedures. We also propose a new approximate calculation. In order to speed up some of the calculations, we propose several fast algorithms for multiple summation.

N >= 1680000, all the results are the same as those in the multinomial distribution.

The computing results showed that the simulations agree closely with the exact results. For small population sizes the critical values and powers of the procedures are different from the corresponding multinomial procedures, but when

Additional Files
jun_liu.jpg (1222 kB)

McMaster University Library