Bias corrected maximum likelihood estimators for the parameters of the generalized normal distribution

Year 2024, Volume: 73 Issue: 4, 1050 - 1071

Hasan Hüseyin Gül , Fatma Zehra Doğru

https://doi.org/10.31801/cfsuasmas.1439744

Abstract

The generalized normal (GN) distribution was defined as a generalization of the normal, Laplace, and uniform distributions, with extensive application areas modeling different data settings. At the same time, its maximum likelihood estimators (MLEs) are biased in finite samples. Since such biases may affect the accuracy of estimates, we consider constructing unbiased estimators for unknown parameters of GN distribution. This article adopts the bias-corrected approach, following the analytical methodology suggested by Cox and Snell [1]. Additionally, we explore both regular biases and parametric Bootstrap bias correction techniques. A comprehensive Monte Carlo simulation is conducted to compare the performances of these estimators in estimating GN parameters. Finally, a real data example is presented to illustrate the application of methods.

Keywords

Bootstrap bias-correction, Cox-Snell bias-correction, generalized normal distribution, maximum likelihood estimators, Monte-Carlo simulation

Supporting Institution

Giresun University, Grnat number: FEN-BAP-A-090323-15

Thanks

We are grateful for the support provided by Giresun University (Grant number: FEN-BAP-A-090323-15) through its Type A project of Scientific Research and Development Projects. Additionally, we thank two anonymous referees and the associate editor for their valuable comments and suggestions, which have greatly improved the paper.

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