Tests of fit for the Gumbel distribution: EDF-based tests against entropy-based tests

Hadi Alizadeh Noughabi; Jalil Jarrahiferiz

doi:10.1080/02664763.2019.1698522

Tests of fit for the Gumbel distribution: EDF-based tests against entropy-based tests

J Appl Stat. 2019 Dec 4;47(10):1885-1900. doi: 10.1080/02664763.2019.1698522. eCollection 2020.

Authors

Hadi Alizadeh Noughabi¹, Jalil Jarrahiferiz²

Affiliations

¹ Department of Statistics, University of Birjand, Birjand, Iran.
² Department of Mathematics, Birjand Branch, Islamic Azad University, Birjand, Iran.

Abstract

In this article, we propose some tests of fit based on sample entropy for the composite Gumbel (Extreme Value) hypothesis. The proposed test statistics are constructed using different entropy estimates. Through a Monte Carlo simulation, critical values of the test statistics for various sample sizes are obtained. Since the tests based on the empirical distribution function (EDF) are commonly used in practice, the power values of the entropy-based tests with those of the EDF tests are compared against various alternatives and different sample sizes. Finally, two real data sets are modeled by the Gumbel distribution.

Keywords: Entropy estimator; Gumbel distribution; Monte Carlo simulation; test power.