ABSTRACT
There are several variations possible in goodness-of-fit testing. Several test statistics which make more specific use of the individual observation values have been proposed. The chi-square statistic provides a general test procedure applicable to both completely specified and composite hypotheses and to complete or censored samples. The Cramer-Von Mises statistic is convenient and sometimes more powerful for testing a completely specified hypothesis. The extreme-value and normal distributions are location-scale distributions, so the likelihood ratio test can be carried out. Several different families of distributions have been discussed as possible probability models. In some cases theoretical considerations may suggest a certain distribution, but it is also important to have statistical techniques available to aid in selecting an appropriate model. One difficulty is that with a small sample size several different distributions may appear acceptable, yet tail probabilities from these distributions may vary considerably.
