Linear Bayes Estimator Of The Extreme Value Distribution Based On Type ? Censored Samples

The Extreme Value distribution is widely applied in risk management,finance,insurance,economics,life experiments and other fields to deal with extreme events.These events are often accompanied by censored data.Type ? censored data is the most common type of censorship types.Based on this,many authors have proposed the study of parameter estimation from the perspective of Bayesian and frequency,such as unbiased estimation,approximate maximum likelihood estimation,etc.,but most of them only give numerical solutions.This paper addresses a linear Bayes method to simultaneously estimate the location parameter and the scale parameter of the EV distribution from type ? censored samples,which combines Bayesian thinking and optimization methods.The estimator has a formula with linear structure which is convenient.To a certain extent,it solves the shortcomings of classical Bayes estimator which has no explicit formula and is difficult to calculate in some cases.We also prove that the superiority of the linear Bayes estimator comparing with the classical frequency unbiased estimator in terms of mean square error matrix criterion.According to the results of numerical experiments,the proposed linear Bayes estimator is very close to the Bayes estimator obtained by the MCMC method,and we also compare the linear approximate Bayes estimator with Tierney and Kadane's approximation by numerical simulations.We finally verified numerically that linear Bayes estimator has obvious advantages compared with maximum likelihood estimator and unbiased estimator for small samples and severely censored samples.Finally,the linear Bayes method is applied to a practical case,and the result shows that the linear Bayes estimator is effective and reasonable.