A New Extension of Generalized Extreme Value Distribution: Extreme Value Analysis and Return Level Estimation of the Rainfall Data

Abstract

This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go-GEV was an alternative flexible distribution for extreme values that fitted with actual data and described the maximum rainfall better than the traditional GEV distribution. The probability density functions of the Go-GEV distribution had various shapes including left-skewed, right-skewed and close to symmetric. Estimation of the return levels of rainfall values in Lopburi Province by the Go-GEV distribution indicated that Buachum Station should be monitored because it had higher precipitation and return levels than Lopburi Station at 2, 5, 10 and 15 years. HIGHLIGHTS The analysis of data with extreme values is complex but ignoring an observation just because it is unacceptable is not best practice. One of the widely used tools in such situations is “Extreme Value Theory” The Gompertz-generalized extreme value (Go-GEV) distribution is a new extension of GEV distribution using deffinition of Gompertz-generalized family of distributions The developed Go-GEV model described the maximum rainfall data better than the GEV distribution because the new extension distribution was more flexible and its probability density function had a more diverse shape, such as both left-skewed, right-skewed and close to symmetrical The developed Go-GEV model is a flexible alternative for applying the model to extreme value data GRAPHICAL ABSTRACT