| The poisson-lomax distribution is the compound Lomax distribution and Poisson distribution of Al-zahrani B in 2014,and a new three-parameter life distribution is obtained,which is the extension of Lomax distribution.At present,there are few researches on this distribution,and the advantages of Bayes analysis make it more and more widely used in recent years.This paper mainly studies Bayes estimation of the parameters of poisson-lomax distribution under different loss functions.Firstly,the research background of poisson-lomax distribution and Bayes estimation,the research status at home and abroad,the theoretical basis of maximum likelihood estimation and Bayes estimation,and the maximum likelihood estimation of three parameters of poisson-lomax distribution are briefly described.Secondly,aiming at the parameter ? estimation problem of Poisson-Lomax distribution,Bayes analysis method is adopted to obtain the Bayes estimation expression of parameters ? under six common loss functions,and R software is used for random simulation.The results show that under six common loss functions,the Bayes estimation value of parameters ? is close to the true value,and the estimation effect is good.Then,according to Poisson-Lomax distribution parameter? estimation problem,using the method of Bayes theorem,under the six commonly used loss function was obtained,the parameter ? of the Bayes estimation expressions,and R software numerical simulation,the results show that the under six commonly used loss function,the Bayes estimate is closer to the true value,including choosing scale entropy loss function and loss function parameters of the Bayes estimates the best effect.Finally,discussed under MLINEX loss function,Poisson-Lomax distribution parameter ? of the Bayes estimation problem,the parameter ? of the prior distribution for the Gamma distribution and no information prior distribution,the Poisson-Lomax distribution Bayes estimation expressions,and the parameter ? of the prior distribution of Gamma distribution,gives three kinds of different parameters of E-Bayes estimation and Multiple Bayes estimation,and the given parameters is obtained in other cases,Bayes estimation,E-Bayes estimation and Multiple Bayes estimation are equivalent. |
