Chi-Square Tests for Comparing Weighted Histograms

TL;DR

This paper introduces generalized chi-square tests for comparing weighted histograms, which are common in Monte Carlo simulations, enabling more accurate statistical comparisons between experimental and simulated data.

Contribution

It proposes new chi-square test generalizations specifically designed for weighted histograms, extending classical methods to handle weights and random event counts.

Findings

Tests effectively compare weighted histograms with different event statistics.

Numerical examples demonstrate the tests' applicability to experimental and simulated data.

The methods improve accuracy in histogram comparison in Monte Carlo simulations.

Abstract

Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of a weighted histogram are considered as a sum of random variables with a random number of terms. Generalizations of the classical chi-square test for comparing weighted histograms was proposed. Numerical examples illustrate an application of the tests for the histograms with different statistics of events and different weighted functions. The proposed tests can be used for the comparison of experimental data histograms with simulated data histograms, as well as for the two simulated data histograms.