# Gap-Measure Tests with Applications to Data Integrity Verification

## TL;DR

This paper introduces max-gap statistical tests for assessing uniformity, demonstrating higher sensitivity than chi-square tests in data integrity verification, with comparable computational complexity suitable for Big Data applications.

## Contribution

The paper proposes a new max-gap test for uniformity that improves sensitivity over chi-square tests and maintains similar computational efficiency for large-scale data analysis.

## Key findings

- Max-gap test outperforms chi-square in detecting deviations from uniformity.
- Max-gap test has same computational complexity as chi-square.
- Applicable for Big Data integrity verification.

## Abstract

In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($\chi^2$), thus allowing the new test to be used in place of or as a complement to $\chi^2$ testing for purposes of distinguishing a larger class of deviations from uniformity. We establish that the proposed max-gap test has the same sequential and parallel computational complexity as $\chi^2$ and thus is applicable for Big Data analytics and integrity verification.