Summary: UNIVERSITY OF REGINA
Department of Mathematics & Statistics
Speaker: Yu (Ally) Zhang
Date: Wednesday, November 16, 2005
Time: 2:30 p.m.
Location: College West 307.18 (Math & Stat Lounge)
Title: Estimation of the bivariate exponential distribution based on the Gamma method
Abstract: In this talk, I will discuss the estimations of BVED (Bivariate Exponential Distribution)
for the paired lifetime data. I use more advanced censoring schemes this time. One is random
censoring, which means the censoring time is not fixed but follows an exponential distribution.
The other is a hybrid censoring scheme, which combines type one and type two censoring together.
Rather than the maximum likelihood method, I found another way of estimating the parameters,
which is called the Gamma Method. Using this method, I obtained the closed-form of estimators
and the asymptotic variances for unknown parameters. I also conduct the hypothesis test for
assessing whether or not the two marginal exponential parameters are equal.
Simulation studies are given with 10,000 replications. The result shows that the proposed test
statistics maintain the level very well, which means that the empirical levels of the test statistics
are very close to the nominal levels of normal distribution and chi-square distribution. I will also
briefly introduce how I generate the data and how the software works by using statistics software