Simulate a probability distribution model by Mathematica

I have a probability distribution function of a life distribution. The empirical test statistics are ready. I need to do a statistical hypothesis for testing exponentiality for the probability distribution under random censoring by simulating random samples from an exponential distribution, using Mathematica, Matlab, or R. Percentiles and power estimates (for Gamma, Weibull, Pareto, and Rayleigh distributions) need to be tabulated. The asymptotic normality of these tests is also tested. (Similar research was published for different distributions).