Physical Sciences and Mathematics Commons^™

Common Moment Sets Of Complementary Graphs, Hang Chen

Dissertations

Two sequences of nonnegative integers have the k^th common moment if they have equal sums of k^th powers. We intend to study common moment sets of the degree sequences of complementary graphs, and similarly, of the score sequences of complementary tournaments.

In Chapter I, we first study common moment sets of arbitrary sequences of nonnegative integers. Some basic concepts are introduced. The relations between characteristic functions and initial common moments are discovered. We extend Hua’s discussion of the Tarry-Escott problem. We conclude that any finite subset of nonnegative integers can be a common moment set of some sequences, and conversely, …

A Progressive Disease Model For Doubly-Censred Bivariate Survival Data That Accommodates Covariate Information, Hilmi F. Yahya

Dissertations

A model for the natural history of a progressive disease is developed. The model has three disease states and can be expressed as the joint distribution of two survival random variables.

Covariate information is incorporated into the model using the proportional hazards model for the marginal distributions. The model will also accommodate data with observations which are censored on one or both of the survival random variables.

The likelihood function for censored data is exhibited for finding the maximum likelihood estimates of the parameters and their standard errors for testing the effects of the covariates. The method used to obtain …