Abstract: Under the weighted p,q symmetric entropy loss function,the Bayesian estimation method is used to estimate the Kumaraswamy distribution parameters,and the general and exact forms of the Bayesian estimation of the parameters are obtained,which proves the acceptability and minimum maximum of the obtained Bayesian estimation.The multi-level Bayesian estimation,E-Bayes estimation and knife-cut Bayesian estimation of the parameters are given.The numerical simulation of Bayes,E-Bayes and knife-cut Bayes estimation of Kumaraswamy distribution parameters is carried out by using R software combined with Metropolis algorithm.The results show that the Bayes estimation under the Jeffreys priors is more accurate than that under the conjugate prior distribution;the estimation properties under the same prior distribution can be better by using the knife cutting method;and the application of E-Bayes estimation can reduce the influence of hyperparameters on the simulation by selecting appropriate constants.

Key words: Kumaraswamy distribution, loss function, Bayesian estimation, admissibility, Metropolis algorithm