The Statistical Analysis And Inference Of A New Distribution

Given a new two parameters distribution whose failure rate function exhibit bathtub shape, and discuss some estimations of the shape parameter and the scale parameter. For the new distribution, we have the following results in the present paper:(1)The moment estimation, the maximum likelihood estimation (MLE) and the inverse moment estimation of parameters are given under the full sample. Meanwhile, we indicate that the inverse moment estimation of the two parameters is existed. After converting the distribution to a shape-scale distribution, the best linear unbiased estimation (BLUE) and the best linear equivalent estimation (BLIE) are derived. And then the precisions of all the estimations are investigated by Monte-Carlo simulations. For the shape parameter, BLUE is much better than other estimations with respect to the MSE. The inverse moment estimation is the worst of all. For the scale parameter, BLIE is the best. The inverse moment estimation is the worst of all. (2)For the multiply type-II sample, the BLUE and BLIE are also discussed, and the approximate maximum likelihood estimation (AMLE) is another one. We compare these three estimations by Monte-Carlo simulation. The AMLE is much better than others as the estimation of the scale parameter. And for shape parameter, BLUE is the best. (3) At the end of this paper, we list one table that contains the coefficient of the BLUE and BLIE. Meanwhile, the interval estimation is proposed with the different pivotal quantities.