On approximation of the distribution for Pearson statistic

2019/05/20 by Nikolai Dokuchaev, Dokuchaev, Nikolai
Computer Science · #62F03 #62G05 #62G10 #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1905.07881

openalex publication_date 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper considers the classical Goodness of Fit test. It suggests to use the Gamma distribution for the approximation of the distribution of the Pearson statistics with unknown parameters estimated from raw data. The parameters of these Gamma distribution can be estimated from the first two moments of the statistic after averaging over a distribution of the unknown parameter over its range. This allows to simplify calculation of the quantiles for the Pearson statistic, as is shown in some simulation experiments with medium and small sample sizes.

Citations

• The Use of Maximum Likelihood Estimates in χ² Tests for Goodness of Fit

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