Tests for Comparing Weighted Histograms. Review and Improvements

TL;DR

This paper reviews chi-square tests for comparing weighted histograms, proposes improvements for better size accuracy, and demonstrates their effectiveness through numerical examples in simulation contexts.

Contribution

It introduces improved chi-square tests for weighted histograms with enhanced size accuracy and provides a comprehensive review and evaluation through numerical examples.

Findings

Improved tests have sizes closer to nominal values.

Numerical examples demonstrate the tests' effectiveness.

Enhanced methods are suitable for simulation-based probability density estimation.

Abstract

Histograms with weighted entries are used to estimate probability density functions. Computer simulation is the main application of this type of histograms. A review on chi-square tests for comparing weighted histograms is presented in this paper. Improvements to these tests that have a size closer to its nominal value are proposed. Numerical examples are presented for evaluation and demonstration of various applications of the tests.