New generalized extreme value distribution with applications to extreme temperature data

Abstract

A new generalization of the extreme value distribution is presented with its density function, having a wide variety of density and tail shapes for modeling extreme value data. This generalized extreme value distribution will be referred to as the odd generalized extreme value distribution. It is derived by considering the distributions of the odds of the generalized extreme value distribution. Consequently, the new distribution is enlightened by not only having all six families of extreme value distributions; Gumbel, Fréchet, Weibull, reverse-Gumbel, reverse-Fréchet, and reverse-Weibull as submodels but also convenient for modeling bimodal extreme value data that are frequently found in environmental sciences. Basic properties of the distribution, including tail behavior and tail heaviness, are studied. Also, quantile-based aliases of the new distribution are illustrated using Galton's skewness and Moor's kurtosis plane. The adequacy of the new distribution is illustrated using well-known goodness-of-fit measures. A simulation is performed to validate the estimated risk measures due to repeated data points frequently found in temperature data. The Grand Rapids and well-known Wooster temperature data sets are analyzed and compared to nine different extreme value distributions to illustrate the new distribution's bimodality, flexibility, and overall fitness.