# A test against trend in random sequences

## TL;DR

This paper introduces a modified Kendall's tau-test that uses sequences with repetitions, including binary sequences, to evaluate randomness, expanding the applicability of the test to more general sequences.

## Contribution

It proposes a new version of Kendall's tau-test that accommodates sequences with repeated elements, broadening the scope of randomness testing methods.

## Key findings

- The modified test can evaluate the randomness of binary and other sequences.
- It extends Kendall's tau-test to sequences with repetitions.
- The method is applicable to a wider class of sequences, including those with repeated elements.

## Abstract

We study a modification of Kendall's tau-test, replacing his permutations of n different numbers by sequences of length n, where repetition is allowed. In particular, binary sequences are included. Random sequences can be tested.