Extension of the one-sample Kolmogorov-Smirnov test

TL;DR

This paper introduces the one-sample OVL-q test, an extension of the Kolmogorov-Smirnov test, with analyzed asymptotic properties and demonstrated improved detection power in some cases.

Contribution

The paper proposes a new goodness-of-fit test extending the Kolmogorov-Smirnov test and analyzes its asymptotic behavior and p-value calculation methods.

Findings

OVL-2 test has higher detection power in certain scenarios

Asymptotic properties of the OVL-2 statistic are established

Numerical experiments validate the test's effectiveness

Abstract

We propose here a new goodness-of-fit test, named the one-sample OVL-q test (q = 1, 2, . . .), which can be considered an extension of the one-sample Kolmogorov-Smirnov test (equivalent to the one-sample OVL-1 test). We have analyzed the asymptotic properties of the one-sample OVL-2 test statistic and enabled the calculation of asymptotic p-values for the test statistic. We further conducted numerical experiments and demonstrated that the one-sample OVL-2 test can sometimes exceed the detection power of conventional goodness-of-fit tests.