Go to  Advanced Search

Parameter estimation in some multivariate compound distributions

Show full item record

Files in this item

Files Size Format Description   View
UBC_1966_A8 S55.pdf 5.317Mb Adobe Portable Document Format   View/Open
 
Title: Parameter estimation in some multivariate compound distributions
Author: Smith, George E. J.
Degree Master of Arts - MA
Program Mathematics
Copyright Date: 1965
Subject Keywords Distribution (Probability theory)
Abstract: During the past three decades or so there has been much work done concerning contagious probability distributions in an attempt to explain the behavior of certain types of biological populations. The distributions most widely discussed have been the Poisson-binomial, the Poisson Pascal or Poisson-negative binomial, and the Poisson-Poisson or Neyman Type A. Many generalizations of the above distributions have also been discussed. The purpose of this work is to discuss the multivariate analogues of the above three distributions, i.e. the Poisson-multinomial, Poisson-negative multinomial, and Poisson-multivariate Poisson, respectively. In chapter one the first of these distributions is discussed. Initially a biological model is suggested which leads us to a probability generating function. From this a recursion formula for the probabilities is found. Parameter estimation by the methods of moments and maximum likelihood is discussed in some detail and an approximation for the asymptotic efficiency of the former method is found. The latter method is asymptotically efficient. Finally sample zero and unit sample frequency estimators are briefly discussed. In chapter two, exactly the same procedure is followed for the Poisson-negative multinomial distribution. Many close similarities are obvious between the two distributions. The last chapter is devoted to a particular common limiting case of the first two distributions. This is the Poisson-multivariate Poisson. In this case the desired results are obtained by carefully considering appropriate limits in either of the previous two cases.
URI: http://hdl.handle.net/2429/37285
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

This item appears in the following Collection(s)

Show full item record

All items in cIRcle are protected by copyright, with all rights reserved.

UBC Library
1961 East Mall
Vancouver, B.C.
Canada V6T 1Z1
Tel: 604-822-6375
Fax: 604-822-3893