Empirical Bayes Problems Research On The Parameter For Rayleigh Distribution

In this paper, we apply Bayes theory and Empirical Bayes theory to thestatistical analysis problems for Rayleigh distribution of the parameter in thecase of independent identically distributed samples. Rayleigh distribution iswidely used in the field of life test、medicine、mechanical design andcommunication engineering，so it is of great practical significance to study it.In chapter one, Bayes approach、Empirical Bayes approach and BayesEmpirical Bayes approach are introduced. At the same time, the history anddevelopment of Empirical Bayes are generalized..In the second chapter, we study Empirical Bayes Estimation for theparameter of Rayleigh distribution. Empirical Bayes Estimation is constructedunder squared loss function. Meanwhile, an example satisfied the condition ispresented.In the third chapter, Bayes Empirical Bayes Estimation for the parameterof Rayleigh distribution is considered. We prove that the Bayes EmpiricalBayes Estimation converges almost surely to Bayes Estimation and theasymptotically optimal property is obtained. At last, a Monte Carlo simulationexperiment is given to verify the asymptotically optimal property of the BayesEmpirical Bayes Estimation.In the fourth chapter，we discuss Empirical Bayes one-side test andtwo-sides test for the parameter of Rayleigh distribution and constructEmpirical Bayes test function of the parameter under the different lossfunctions. Furthermore, the asymptotically optimal property and thecorresponding convergence rates are achieved under the suitable conditions.In chapter five，the summary and outlook are given.