Testing of Distribution Functions from Complex Sample Surveys

Abstract

Testing the parametric family of distributions is a classical problem in theoretical and applied statistics. However, when the sample is selected with unequal selection probabilities which are related to the values of the response variable, standard methods no longer apply. In this article we consider two alternative approaches for taking account of the sample selection effects. Under the first approach, the range of the response variable is divided into a fixed number of intervals and large-sample Wald statistics and other related statistics are constructed from design-based estimators of the interval probabilities. Under the second approach, the parametric distribution of the sample data is extracted as a function of the hypothesized population distribution and the sample inclusion probabilities. The extracted distribution is then tested using standard test statistics. The two approaches are compared in a simulation study which indicates that the second approach performs better overall in terms of the achieved significance levels and powers against alternative distributions considered.