Skew generalized extreme value distribution: Probability-weighted moments estimation and application to block maxima procedure

ABSTRACT

Following the work of Azzalini (1985 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Stat. 12:171–178.Web of Science ®] , Google Scholar] and 1986 Azzalini, A. (1986). Further results on a class of distributions which includes the normal ones. Statistica 46:199–208. Google Scholar]) on the skew-normal distribution, we propose an extension of the generalized extreme value (GEV) distribution, the SGEV. This new distribution allows for a better fit of maxima and can be interpreted as both the distribution of maxima when maxima are taken on dependent data and when maxima are taken over a random block size. We propose to estimate the parameters of the SGEV distribution via the probability-weighted moment method. A simulation study is presented to provide an application of the SGEV on block maxima procedure and return level estimation. The proposed method is also implemented on a real-life data.