Document Type


Date of Award


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Antai Wang

Second Advisor

Wenge Guo

Third Advisor

Yixin Fang

Fourth Advisor

Sundarraman Subramanian

Fifth Advisor

Zhi Wei


This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is proposed as well, and some simulation studies are performed to demonstrate our parameter estimation method.

The second part is relevant to a new statistic proposed to estimate the survival function where left censoring exists. The derivation of this estimator is a little similar to that of the well-known copula-graphic estimator. The simulation results indicate the difference of performance between it and Left Kaplan Meier estimator when dependent censoring occurs.



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