Statistical Analysis Of Generalized Exponential Distribution With Two Parameters

The paper gives a new generalized two-parameter exponential distribution. We study this distribution with respect to the following aspects:(1)The properties of the kth moments and the order statistics of this distribution are introduced. The graphs of its density and hazard functions under different values of parameters are obtained.(2)The moment estimation, the maximum likelihood estimation, the best linear unbiased estimation, the best linear equivalent estimation and the interval estimation are given under the full sample. Meanwhile, we discuss the existence of the maximum likelihood estimation. The precisions of the best linear unbiased estimation, the best linear equivalent estimation and the moment estimation are investigated by Monte-Carlo simulation. It shows that the moment estimation is the best based on the criterion of the mean square error.(3) The best linear unbiased estimation, the approximation maximum likelihood estimation and the interval estimation are given under the type-Ⅱ sample. We compare the best linear estimation and the approximation maximum likelihood estimation by Monte-Carlo simulation based on the criterion of mean square error, the result shows that the best linear biased estimation is better than the approximation maximum likelihood estimation.