A New Two-parameter Distribution, Statistical Inference

We give a new two-parameter life distribution in this paper. At the same time, the related statistical analysis for this new distribution is given. We have the following results: (1) For the full sample, the moment estimation, the maximum likelihood estimation and the inverse moment estimation are derived and compared by the Monte-Carlo simulation. The corresponding nature of the maximum likelihood estimation function is indicated. And also, detailed theoretical proof of the inverse moment estimation is given for its existence and uniqueness. (2) For the incomplete sample, the maximum likelihood estimation and the inverse moment estimation are derived and compared by the Monte-Carlo simulation,nature of the maximum likelihood estimation function also is given in the paper, at the same time, detailed theoretical proof of the inverse moment estimation is given for its existence and uniqueness. (3)When one parameter is known and the other is unknown, the corresponding theoretical explanation is discussed, and the related interval estimation is given by the Central Limit Theorem and calculated by the Monte-Carlo simulation.