A goodness of fit test for the Pareto distribution in the presence of Type II censoring, based on the cumulative hazard function

A goodness of fit test for the Pareto distribution, when the observations are subjected to Type II right censoring is proposed. The test statistic involves transformations of the original data and is based on the nonparametric Nelson–Aalen estimator of the cumulative hazard function. By Monte Carlo simulation, the empirical distribution of the test statistic is obtained and the power of the test is investigated for some alternative distributions. The power is compared with adaptations for Type II censored data of the Crámer–von Mises and Anderson–Darling tests, and a test based on Kullback–Leibler information. For some alternative distributions with monotone decreasing hazard function, the proposed test has higher power. The methodology is illustrated by reanalyzing two published data sets.