Probability Distribution of Extreme Events in Complex Systems: Application to Climate Data

It has been observed that the statistical structure of certain climate vectors, such as wind speed versus air density and temperature versus humidity, may exhibit more than one mode due to the complexity of climate systems. This study proposes a new bivariate extreme value distribution, called the transformed symmetric logistic extreme value distribution, which can capture the multimodal characteristics of the joint distribution of extreme observations in complex systems. We derive some of its properties, such as marginal distributions, tail indices, conditional distribution, and P(Y<X). The parameters of the new distribution were estimated using the maximum likelihood method. The applicability of the proposed model is illustrated with climate data, including the analysis of the result P(Y<X).