The Statistical Analysis Of Two-parameter Exponential Distribution

Two parameter exponential distribution is not only an important distribution in life testing,but also act as a representative distribution of location-scale population,the study to it has a certain significance.This thesis starting from the study of order statistics belong to two parameter exponential distribution with it properties and distributions.From single order statistic distribution to different order statistics joint distribution.Then the distribution function of1XXn- is given,which show a same conclusion to exponential distribution.We make a special effort to introduce the mutual independence of order statistics.Further more,we give a detailed description of the expectation, variance, co-variance to different order statistics by adopting the general to the specific method.Then,two available statistical analysis are given,which consisted of simple random sampling and ranked set sampling.In simple random sampling,we give the estimation of two parameter exponential distribution,from the full sample experiment to type II censoring,all include maximum likelihood estimation,minimum variance unbiased estimation,and best invariant estimation.At the same time another loss function have been mentioned to best invariant estimation.Then,give the simulation of the three estimators which appeared in this thesis by using the Monte Carlo method.In simple random sampling,we also give probability chat method and likelihood ratio test of two parameter exponential distribution.In this part we give a detailed description of two parameter exponential distribution in likelihood ratio test,and the test function j)(x are given.In the last chapter of the thesis,we first show the specific process of ranked set sampling,and make the conclusion that when compare the variance of X,ranked set sampling is better than simple random sampling.Then we deduce the estimation of two parameter exponential distribution under ranked set sampling,however,only include maximum likelihood.Finally find out the The modified maximum likelihood estimator tol and m.