A study of methods for estimating in the exponentiated Gumbel distribution

Abstract

The exponentiated Gumbel model has been shown to be useful in climate modeling including global warming problem, flood frequency analysis, offshore modeling, rainfall modeling and wind speed modeling. Here, we consider estimation of the PDF and the CDF of the exponentiated Gumbel distribution. The following esti- mators are considered: uniformly minimum variance unbiased (UMVU) estimator, maximum likelihood (ML) estimator, percentile (PC) estimator, least squares (LS) estimator and weighted least squares (WLS) estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others.

Keywords

• Uniform minimum variance unbiased estimator; Maximum likelihood estimator; Least squares estimator;Weight least squares estimator; Percentile estimator; Model selection criteria; Exponentiated Gumbel distribution.