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Keywords:
generalized extreme value distribution; regression method; Box–Cox transformation; profile likelihood
generalized extreme value distribution; regression method; Box–Cox transformation; profile likelihood
Summary:
This study focuses on parameter estimation for the generalized extreme value distribution (GEVD) using the regression method described by [Van2012median]. A regression equation is derived from the cumulative distribution function and the scale parameter is estimated by applying the iterative re-weighted least squares in this regression equation. For estimating the shape parameter, a profile likelihood is constructed based on this regression equation. A comparison study of the regression method with other existing estimators derived from the method of moments, maximum likelihood, probability-weighted moments, l-moments, and maximum product spacing is performed for the GEVD. Also, the left truncated GEVD is considered and the behaviour of its hazard function is studied. The parameter estimates of the left truncated GEVD is also derived using the regression method. An extensive simulation study is conducted and the efficiencies of the estimation techniques are analysed. The bootstrap confidence intervals for the estimators are also constructed. Finally, a real data analysis is carried out to illustrate the applicability of the models and estimation techniques.
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