A goodness of fit test for the Pareto distribution with progressively type II censored data based on the cumulative hazard function (Q2292024)

The authors consider progressive type II censoring schemes. At the beginning of an experiment, \(n\) objects are placed. When the \(i\)-th \((i=1,2,\dots,m)\) failure is observed, the failure time \(X_i\) is recorded and \(R_i\) individuals are removed, where \(R=(R_1,R_2,\ldots,R_m)\) is determined beforehand and satisfied that \(n=m+\sum_{i=1}^mR_i.\) While with the complete lifetime sample \(R_1=R_2=\cdots=R_m=0,\) with the traditional type II censored sample \(R_1=R_2=\cdots=R_{m-1}=0,\) \(R_m=n-m.\) Based on this scheme, a goodness-of-fit test process for the Pareto distribution with two parameters is developed. The empirical distribution of the test statistics is obtained. The distribution of the test statistics is independent of the selection of the parameters but related to the censoring percentage. Using the Monte Carlo simulation, the authors compare the power of the proposed test statistic with that other test statistics, with monotonic and non-monotonic hazard functions. Examples are provided to illustrate the proposed test.