A New Class of Generalized Extreme Value Distribution and Application under Alpha Power Transformation Method (European Journal of Pure and Applied Mathematics, 2023)
This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness.
Keywords: Extremes value theory; Generalized extreme value distribution; Alpha Power Transformation Method; Return level; Maximum likelihood estimation