Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literure can be found on tests for assessing their goodnes of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicitly use of the mixture structure. In...

How can researchers test for heterogeneity in the local structure of a network? In this paper, we present a framework that utilizes random sampling to give subgraphs which are then used in a goodness of fit test to test for heterogeneity. We illustrate how to use the goodness of fit test for an analytically derived distribution as well as an empirical distribution. To demonstrate our framework,...

An increasingly important problem in the era of Big Data is fitting data to distributions. However, many stop at visually inspecting the fits or use the coefficient of determination as a measure of the goodness of fit. In general, goodness-of-fit measures do not allow us to tell which of several distributions fit the data best. Also, the likelihood of drawing the data from a distribution can be...