Bayes Statistical Inference Of Parameters For Inverse Rayleigh Distribution

The inverse Rayleigh distribution plays an important and extensive role in the study of life test and reliability.At present,the problem of statistical inference based on this distribution is also in constant improvement and development.In the theory of statistical inference,Bayesian analysis is one of its important contents,its application has almost penetrated into the various fields of statistics,the use of Bayes theory of some basic content,the parameters of the relevant statistical inference research is modern statistics An important method of extrapolation.This paper aims to study the Bayesian statistical inference problem of inverse Rayleigh distribution.This paper mainly includes four parts.The first part mainly introduces the development,research background and application of Bayesian theory.The main results of the paper are in the second part to the fourth part,in which the second part focuses on the estimation of the inverse Rayleigh distribution parameters under several different loss functions,including: 1.When the prior distribution of parameters takes the gamma distribution,the posterior density function of the inverse Rayleigh distribution is obtained.2.Based on the theoretical method,the parameters are estimated by symmetric entropy loss function,Q symmetric entropy loss function,Mlinex loss function and composite LINEX symmetry loss function,which proves its admissibility and makes numerical simulation.In the third part,the minimum maximal(Minimax)estimation of the parameters in the inverse Rayleigh distribution under the Mlinex loss function and the weighted square loss function is obtained under the Jefferys non-information prior distribution.In the fourth part,based on the NA sample,the empirical Bayesian test function of the inverse Rayleigh distribution parameter is obtained,and the asymptotic property and the convergence speed of the Bayesian test function are obtained.