Research On Parameter Estimation Of Compound Rayleigh Distribution Based On Bayes Analysis

Parameter estimation is not only a classical problem in statistical research,but also widely used in various fields.The compound Rayleigh distribution is a fixed distribution of a parameter in the three-parameter Burr distribution.Compared with the three-parameter Burr distribution,there are fewer parameters in the composite Rayleigh distribution,which is more beneficial to the study of the properties of the distribution.Some scholars study the parameter estimation of the distribution under complete data,which are characterized by classical estimation method and Bayes estimation method,respectively.However,no scholars have studied the parameter estimation of compound Rayleigh distribution under missing data types.Compound Raleigh distribution is a kind of distribution with obvious characteristics at the back and end of the peak,which is loved by related researchers in medicine,product life and menstrual fusion.In order to understand the compound Rayleigh distribution more deeply,the parameter estimation problem of the compound Rayleigh distribution will be studied in this paper.This paper is divided into five parts.The first part mainly introduces the research background of composite Rayleigh distribution parameter estimation,and briefly summarizes the research status of parameter estimation at home and abroad;the second part mainly introduces the preparatory knowledge of the research content of the article.The main research contents are from the third chapter to the fifth chapter,in which the third chapter mainly aims at the parameter estimation of the compound Rayleigh distribution under the bilateral definite truncated data sample;the fourth chapter mainly studies the parameter estimation problem of the compound Rayleigh distribution under the stepwise II censored data sample;the fifth chapter mainly aims at the parameter estimation problem under the mixed normal-compound Rayleigh distribution model,and draws the following conclusions:(1)In the case of bilateral fixed truncated samples,the maximum likelihood estimation method and Bayes estimation method are used to estimate the parameters,and then the square loss function,entropy loss function and symmetric entropy loss function are selected as loss functions to estimate the parameters.The simulation results show that the symmetric loss function is closer to the real value than the estimated value of square loss function and entropy loss function.(2)Under the stepwise type ? censored data,the maximum likelihood estimation method and Bayes estimation method are used to estimate the parameters,and then the square loss function and symmetric entropy loss function are selected in the Bayes estimation method to compare the advantages of square loss function and symmetric entropy loss function in parameter estimation.The simulation results show that the estimated value of symmetric entropy loss function is closer to the real value under this data type.(3)When the actual data are complex,the mixed normal-compound Rayleigh distribution model is used to estimate the parameters,the maximum likelihood estimation method and EM algorithm are used to estimate the parameters,and the performance trend of a Chuanjin Citic 500 index fund is selected as the example data to analyze.Solving the proportion of the mixed model in the actual problem is the key to the mixed model problem.