Tests for Comparing Weighted Histograms. Review and Improvements
Nikolai Gagunashvili

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.
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