Homogeneity and scale testing for small samples with censored and missing data

In this section we provide the exact likelihood ratio testing procedure of the shape parameter of the Pareto and scale parameter of generalized gamma distribution when there is a missing time-to-failure information. This is an important result because the asymptotical χ2-test is oversized an thus inappropriate especially for small merged samples. The small merged samples can arise also for a large sample sizes when individual times-to-failure are not available. Data sets with missing time-to-failure data can arise from field data collection systems. Real data and simulated examples are provided to illustrate the methods discussed.