Goodness-of-fit tests for the pareto and lognormal distributions based on multiply truncated samples

This article considers the situation where, in the most general case, each observation in a sample has been “truncated” below at a different, but known value. Each observation is truncated in the sense that, had it been 1ess than the truncati on point, it would not have appeared in the sample. A goodness-of-fit test based on Gnedenko’ F statistic is developed to test the hypothesis that the underlying distribution is Pareto against the alternative of lognormality. The Chi-square and Kolmogorov tests are adapted to test the hypothesi s of lognormality with unspecified alternative. The application of these techni ques to the analysis of insurance claim data is discussed.