Title: Bayesian Inference for the System Lifetimes under Frank Copulas

Abstract:
    The lifetime of a coherent system of n components with identical exponential lifetimes is considered. We derive its density function when the joint distribution of these n components is represented by the Frank copulas. Then the likelihood function of the dependence parameter in the copulas and the rate parameter of the component lifetime based on a random sample of m system lifetimes is constructed. Unfortunately the likelihood is an unbounded function of the dependence parameter and maximum likelihood estimator does not exist. Therefore we analyze the data via Bayesian inference with given prior distributions of the parameters. The posterior distribution of the unknown parameters is obtained by the Metropolis-Hastings-within-Gibbs algorithm. The purposed method will then be illustrated by a simulated example.
Lecturer: Chan Ping Shing Ben
Date/Time: 24th May, 2019  15:00-16:00
Location: Room 706, CEM Building, Jiangjun Rd. Campus

Brief introduction of the lecturer:
    Dr. Chan obtained his Ph.D. degree from McMaster University Canada in 1993. He has joined the Chinese University of Hong Kong since 1992 and he now is associate professor in the Department of Statistics. Dr. Chan’s main research interests are survival analysis and reliability statistics, and he has published more than 40 papers in many famous journals including Technometrics, EJOR, IISE, NRL. He also is the Director of MSc Data Science and Business Statistics Program.