Studies in the lifetimes of the organisms and products are often the main researches topics in the nature and industries. The situation that we can not obtain the complete samples may occur from time to time in our real life due to several reasons. For example, we have to end the testing in advance because of the neglect and failure of mankind or the consideration of cost and time; in some medical clinical experiment, some patients might not proceed the experiments for some specific reasons, or the testing itself may come to an end ahead of time in order not to cause any possibility of danger to people undertaking it. The Type II progressive censoring with random removals is thus arisen. This research is mainly concentrating on the statistical analysis of two-parameters Gompertz distribution and Rayleigh distribution under type II progressive censoring with random removals. In this thesis, we establish the confidence interval , confidence region, and hypothesis testing for the parameters of Gompertz distribution under the type II progressive cencered samples with binomial and random removals separately. In addition, we also establish the shortest confidence interval and hypothesis testing for the parameter of Rayleigh distribution under the type II progressive censored samples with binomial and random removals. Finally, we compare the performances of the proposed pivotal quantities based on the length of confidence interval, the area of confidence region, and the power of hypothesis testing.