比较加权直方图的卡方检验
Chi-Square Tests for Comparing Weighted Histograms
摘要：
在蒙特卡罗模拟中，加权直方图常用于概率密度函数的估计。它们是作为具有权重的随机事件的随机实验的结果而获得的。本文将加权直方图的面元内容看作是随机数项的随机变量之和。对经典的加权直方图比较卡方检验进行了推广。数值算例说明了不同事件统计量和不同加权函数的直方图检验的应用。所提出的测试可用于实验数据直方图与模拟数据直方图的比较，以及用于两个模拟数据直方图的比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
