Exact Non‐parametric Confidence Intervals for Quantiles with Progressive Type‐II Censoring

It is shown how various exact non‐parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type‐II censoring, which is a kind of evolutionary right censoring. Ordinary type‐II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two‐sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type‐II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well‐known properties of ordinary order statistics.