On approximation of the distribution for Pearson statistic
Statistics Theory
2019-05-21 v1 Statistics Theory
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.
Cite
@article{arxiv.1905.07881,
title = {On approximation of the distribution for Pearson statistic},
author = {Nikolai Dokuchaev},
journal= {arXiv preprint arXiv:1905.07881},
year = {2019}
}