Goodness-of-fit tests for the two parameter Weibull distribution

Abstract

The Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics are considered for testing the goodness of fit of the two-parameter Weibull distribution. The statistics for testing the goodness of fit of a completely specified distribution are modified by replacing the Weibull parameters by their maximum likelihood estimates. Also considered are two tests due to Mann, Scheuer, and Fertig (1973), and to Smith and Bain (1976). Tables of critical values are presented for the Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics. The results of a power study are presented comparing all five tests.

Keywords:

• Kolmogorov-Smirnov
• Anderson-Darling
• Cramér-von Mises
• power
• critical values