A Goodness-of-Fit Test for the Two Parameter vs. Three Parameter Weibull; Confidence Bounds for ThreshoId

Abstract

An investigation is described herein of modifications of the two-parameter Weibullgoodness-of-fit test of Mann, Scheuer and Fertig (1973). It is assumed that the sole alternative of interest is any three-parameter Weibull distribution. The power of candidate test statistics is investigated, therefore, only under various three-parameter Weibull alternative hypotheses. It is found that for a fixed selection of gaps (differences of adjacent order statistics) used in the numerator and in the denominator of the approximately F dist ributed test statistic, nothing is gained by weighting the gaps in order to minimize the variances and thus to maximize the numbers of degrees of freedom. A test statistic which is a modified version of that of Mann, Scheuer and Fertig is shown to have higher power under three-parameter Weibull alternatives, and a simple method for approximating critical values of the test statistic is described. The test statistic is shown to be a monotone function of an unknown threshold (location...