Date of Completion

Spring 4-29-2022

Thesis Advisor(s)

Jun Yan

Honors Major



Statistical Theory


The Kolmogorov–Smirnov (KS) test is one of the most popular goodness-of-fit tests for comparing a sample with a hypothesized parametric distribution. Nevertheless, it has often been misused. The standard one-sample KS test applies to independent, continuous data with a hypothesized distribution that is completely specified. It is not uncommon, however, to see in the literature that it was applied to dependent, discrete, or rounded data, with hypothesized distributions containing estimated parameters. For example, it has been "discovered" multiple times that the test is too conservative when the parameters are estimated. We demonstrate misuses of the one-sample KS test in three scenarios through simulation studies: 1) the hypothesized distribution has unspecified parameters; 2) the data are serially dependent; and 3) a combination of the first two scenarios. For each scenario, we provide remedies for practical applications.