# On a transform of the Vincze-statistic and its exact and asymptotic distribution

## TL;DR

This paper introduces a new nonparametric test based on a transform of the Vincze-statistic for two-sample problems, providing exact and asymptotic distributions, with potential applications to one-sided and two-sided tests.

## Contribution

It develops a novel transform of the Vincze-statistic and derives its exact and asymptotic distributions, extending the applicability to two-sided tests.

## Key findings

- Derived exact distribution of the transform T
- Established asymptotic distribution of T
- Proved limit theorem for the two-sided problem

## Abstract

We motivate a new nonparametric test for the one-sided two-sample problem, which is based on a transform T of the Vincze-statistic (R,D). The exact and asymptotic distribution of T is derived. The fundamental idea can also be applied to the two-sided problem. Here too, a limit theorem can be proved.