Research On The Characteristics And Statistical Inference Of A Class Of Generalized Exponential Distributions

The generalized exponential distribution that Gupta,R.D.and Debasis Kundu proposed in 1999 has many good properties.To a certain degree,it overcomes the defect of "no memory" which exponential distribution has,it's widely used in reliability research.Based on the predecessors' work,in this article,we constructe a new function.From the formal point of view,it's much like the distribution function of two-parameter generalized exponential distribution,and we study it from the following aspects.First part,we verify that the constructed function satisfies the distribution function.That is to say this function satisfies three conditons,such as monotone decreasing property,global boundedness and right continuity at any point.Moreover,we caculate the failure rate function of the distribution and analyse these images.Second aspect,the K-Order Moment of this distribution is calculated out and we know that the K-Order Moment is a polynomial about the two unknown parameters.In the article,the density function of the distribution is calculated.We also research the Order statistics and its properties,three cases of order statistics to meet the degree of correlation of variables are demonstrated in detail,for example TP2 dependence,right tail increasing(RTI)and left tail decreasing(LTD).Meanwhile,we get some theories about it.Third,in the full sample,five different parameter estimation methods are proposed.In the first place,according to the thought that the First-Order or Second-Order sample moment is equal to the total First-Order or Second-Order moment,we get the moment estimation.Next,based on maximum likelihood principle,we obtain the maximum likelihood estimation,and prove the existence and uniqueness theorem of maximum likelihood estimator under certain conditions.Again,the best linear unbiased estimation is obtained by using order statistics,but the result is not simple,we also obtain the optimal equivariant estimation of unknown parameters.Finally,we give the interval estimation of unknown parameters by using the pivot variable method.The fourth,we extend the generalized exponential distribution with two parameters and get a more general expression.Monotone decreasing property,global boundedness and right continuity at any point are verified.We calculate the K-Order Moment,mathematical expectation and variance,moreover,the relationship between the two coefficients of one of the parameters has been found out.Under different parameters,we draw out the density function image of the distribution.We obtain expressions about the moment estimation and the maximum likelihood estimation.At the end of this article,we make a summary about the the properties of two-parameter exponential distribution and give some opinions on the further work.