Test of exponentiality with shift based on conditional distribution relative to sufficient statistics

Abstract

Goodness-of-fit tests for composite hypotheses is an open research topic in statistics. Basically, there are two strategies to construct such a test. One strategy relies on parameter estimation and Monte-Carlo technique to obtain p-values, the other technique searches for characterizations of parametric distribution families and constructs a test statistic from such a characterization. In this talk we discuss and construct a goodness-of-fit test based on the conditional distribution of the sample given sufficient statistics, for the exponential distribution with a shift with both parameters unknown