The Bayes Estimation And The Maximum Likelihood Estimation Of The Rayleigh Distribution

The Rayleigh distribution is an important continuous life distribution, which iswidely used in acoustics, medical research, quality control, communications andreliability engineering, aerospace and other fields. The sample data can not be fullyobtained in the study due to various reasons, and therefore how to estimate theparameter of the Rayleigh distribution in the case of incomplete data is a problemworthy of study. At the same time, we also see that the study of the HPD intervals ofthe parameter of a distribution is not so much, which is solved with the method ofconditional extreme. Researches about the Bayes estimation and maximum likelihoodestimation of the parameter of the Rayleigh distribution are not integrated. In allusionto issues above, estimation and Hypothesis testing of the parameter of the Rayleighdistribution are studied.Firstly, the interval estimation of the parameter of the Rayleigh distribution isstudied. The general Bayes interval is given, and the HPD interval which is solvedwith the method of conditional extreme is given too. Then calculated and comparedthe length of each interval by the Matlab.Secondly, the parameter estimation of the Rayleigh distribution under type-Icensored is studied. Bayes estimation’s general form and precise form of theparameter are given under the compound Linex symmetric loss function and Gammaprior distribution. Then, above results are simulated by the Matlab.Finally, the maximum likelihood estimation of the parameter of the Rayleighdistribution under the condition of type-I censored and missed data existing at thesame time is studied. The strong consistency and asymptotic normality of theestimation are proved, when the sample size tends to infinity. Then the hypothesistesting and confidence interval are given too. At last, above results are proved by theMatlab.