A note on smooth tests of goodness of fit for location-scale families

Abstract

In this note, we show that the test statistic given by Rayner & Best (1986) for Neyman's (1937) smooth test of goodness of fit for location-scale families does not, in general, have the alleged chi-squared distribution. As a result, gross error may result from using their test strategy. The size of this error is obtained for the logistic distribution.