Study On Stochastic Order Of Parameter Estimates Of Exponential Distribution

In reliability theory and practical reliability engineering,exponential distribution is one of the most widely used distribution in life test.Some statisticians have studied the order preserving property of the maximum likelihood estimators of the exponential distribution parameters under the type I and type II censoring samples,and further studied the order preserving property of the parameters estimators of the exponential distribution under the time censoring samples,the fixed censoring samples and the successive censoring samples.First of all,the order preserving problem of the mean estimators of exponential distribution with single or double parameters is studied based on the time censored samples.Among them,the mean estimation of distribution parameters is calculated by the maximum likelihood estimation method.Order preserving is the random order relation of random variables.The probability of maximum likelihood estimators of two distribution parameters is calculated and compared,and the maximum likelihood estimators of parameters meet the random order relation.Secondly,it studies the order preserving property of the mean estimators of single and double parameter exponential distribution parameters under the censored samples.The method used is to find the maximum likelihood estimators of two independent exponential distribution parameters respectively,and then calculate the distribution density of the maximum likelihood estimators of the parameter mean according to the joint probability density of the truncated samples.Finally,the comparison is carried out to obtain the random order relationship.Finally,based on the successive censoring samples,the random order relation of the parameter mean estimators of the two parameter exponential distribution is studied.It is also necessary to find the maximum likelihood estimators of two independent two parameter exponential distribution parameters,find their distribution density and compare them to get the random order relationship.