Tests of Fit Based on Normalized Spacings.
STANFORD UNIV CA DEPT OF STATISTICS
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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 andor 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. Additional keywords goodness of fit, leaps, covariance, computations, order statistics. Author.
- Statistics and Probability