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

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

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