Tests of Fit Based on Normalized Spacings

摘要

Normalized spacings provide useful tests of fit for many suitably regular continuous distributions; attractive features of the tests are that they can be used with unknown parameters and also with samples which are censored (Type 2) on the left and/or right. A transformation of the spacings leads, under the null hypothesis, to a set of z-values in 0,1; these are not however, uniformly distributed except for spacings from the exponential or uniform distributions. Statistics based on the mean or the median of the z-values have already been suggested for tests for the Weibull (or equivalently the extreme value) distribution; we now add the Anderson-Darling statistic. Asymptotic theory of the test statistics is given in general, and specialized to the normal, logistic and extreme-value distributions. Monte Carlo results show the asymptotic points can be used for relatively small samples. Also, a Monte Carlo study on power of the normal tests is given, which shows the Anderson-Darling statistic to be powerful against a wide range of alternatives; it is possible for the mean and median to be not consistent and even biased. (Author)