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A COMPARATIVE STUDY OF GOODNESS-OF-FIT TESTS FOR THE GUMBEL DISTRIBUTION

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  • H. Alizadeh Noughabi
H. Alizadeh Noughabi
Department of Statistics, University of Birjand, Birjand, Iran
DOI: https://doi.org/10.26398/IJAS.267

Published 2024-12-21

Keywords

  • Gumbel distribution,
  • Kullback-Leibler information,
  • Goodness-of- fit tests,
  • Test power,
  • Monte Carlo simulation

How to Cite

Noughabi, H. A. (2024). A COMPARATIVE STUDY OF GOODNESS-OF-FIT TESTS FOR THE GUMBEL DISTRIBUTION. Italian Journal of Applied Statistics. https://doi.org/10.26398/IJAS.267

Copyright (c) 2024 H. Alizadeh Noughabi

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The Gumbel distribution is one of the most used models to carry out risk analysis in extreme events, in reliability tests, and in life expectancy experiments. In this article, we extend the general statistics for goodness-of-fit tests proposed by Noughabi (2019), specifically focusing on the Gumbel distribution. Our approach utilizes a new estimate of Kullback-Leibler information to develop a goodness-of-fit test. The properties of the test statistic are presented, and the unknown parameters of the Gumbel distribution are estimated by the maximum likelihood method. Critical points of the proposed test statistic are obtained through Monte Carlo simulation. A simulation study is conducted to evaluate the power of the test and compare its performance with existing tests. Finally, two real data examples are presented and analyzed.

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