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Title: Bayesian inference for the system lifetimes under Gumbel copulas Authors:  Ping Shing Ben Chan - The Chinese University of Hong Kong (Hong Kong) [presenting]
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 Gumbel 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 by assuming the prior distribution of the parameters to be known. The posterior distribution of the unknown parameters is obtained by the Metropolis-Hastings-within-Gibbs algorithm. The proposed method will then be illustrated by a simulated example.