Modeling of Reversed Fréchet Distribution under Linear Normalizing

Abstract

Extreme value theory (EVT) is becoming increasingly important as a suitable model of extreme events to represent phenomena in various fields of applications where extreme values may appear and have detrimental effects. In EVT, the Reversed Fréchet (RF) distribution is a special case of the Reversed generalized extreme value distribution (RGEVD) for modeling extreme data under linear normalizing. The purpose of this paper is divided into four objectives: Firstly, we discuss the practical aspects of the two methods that belong to the domain attraction of RF distribution. The second objective is to use RF distribution to model the behavior of two extreme air pollutants. The third objective is based on a diagnostics plot and hypothesis testing used to evaluate an appropriate shape of the tail distribution. Lastly, for the fourth objective, we attempt to obtain the return level period (RLP) that is expected to be exceeded. Maximum likelihood estimation (MLE) is derived and used to estimate the parameters of RF distribution. The results show that applications are significant for modeling by RF distribution in all cases of two air pollutants. Software that was used in all computations and graphics is the R statistical program with packages fExtreme and ismev.