Modified Anderson-Darling and Cramer-Von Mises Goodness-of-Fit Tests for theNormal Distribution

摘要

New techniques for calculating goodness-of-fit statistics for normaldistributions with parameters estimated from the sample are investigated. Samples are generated for a Normal(0,1) distribution. Critical values are calculated for five modifications to the Anderson-Darling statistic and five modifications to the Cramer-Von Mises statistic. An extensive power study is done to test the power of the new statistics versus the power of the unmodified statistics. Powers of six of the new statistics show minimal to no improvement, two of the new statistics show a marked decrease in power, and two of the new statistics show an overall increase in power over the unmodified statistics. One of these two improved statistics was the obvious better of the two, and it was a modification to the Anderson-Darling statistic. Complete tables of critical values for sample sizes n=4 through n=50 are included for all Anderson-Darling and Cramer-Von Mises statistics, both modified and unmodified.