Chi-Square Tests of Fit for Type II Censored Data

Abstract

The theory of general chi-square statistics for testing fit to parametric families of distributions is extended to samples censored at sample quantiles. Data-dependent cells with sample quantiles as cell boundaries are employed. Asymptotic distribution theory is given for statistics in which unknown parameters are estimated by estimators asymptotically equivalent to linear combinations of functions of order statistics. Emphasis is placed on obtaining statistics having a chi-square limiting null distribution. Examples of such statistics for testing the fit of Type II censored samples to the negative exponential, normal, two-parameter uniform and two-parameter Weibull families are given.