Unified Extreme-Value Distribution

Abstract

A new unified extreme-value (UEV) distribution is proposed that combines EV-1 (Gumbel), EV-2 (Frechet), and EV-3 (Weibull) distributions to better replace the generalized extreme-value (GEV) distribution in that sense. Two simple methods, one graphical and other objective, are devised for estimating parameters of the new UEV, with the diagnostic property of identifying the concerned extreme-value distribution implicitly from the data series used. Its application on illustrative examples suggests an ease of application, reliable estimates of parameters, full transparency in the estimation process, and outperformance of widely used computationally and mathematically more complex methods, e.g., method of moments, maximum likelihood, and probability weighted moments, on GEV and EV distributions, resulting in savings of time and resources. Parameter determination and application of the UEV distribution can even be worked out on a spreadsheet. A new concept and quantification of a deterministic confidence limit is also proposed for its easy application to avoid and replace the tedious process with statistical hypothesis-testing involved in the currently used probabilistic confidence interval. The new UEV, estimation methods, and deterministic confidence limit will be of help to field engineers and practitioners.