Exact goodness-of-fit tests for shape-scale families and type II censoring

摘要

A survey of statistical methods for validation of shape-scale families of probability distributions from type II censored samples is given. We propose “integrated likelihood ratio tests” which are modifications of Zhang’s tests from complete to type II censored data. We also give modifications of Cramér–von-Mises and Anderson–Darling tests using integration with respect to non-parametric estimators of the cumulative distribution function. Explicit formulas for modified chi-squared tests from censored data with data driven choice of partitioning are given. Powers of tests against most used alternatives to the Weibull, loglogistic and lognormal distribution are compared.