A New Distribution for Extreme Value Analysis

The shape of the commonly used distributions in extreme value analysis is determined by either a specific functional form or a shape parameter. In this paper, we develop a family of distributions which uses two parameters to determine the shape: a balance parameter to control symmetry and a tail order parameter to control the thickness of the tail and modes. Each member in this family has closed forms for its density, cumulative distribution, and quantile function. We discuss the maximum likelihood and minimum distance estimation of the unknown parameters and illustrate the usefulness of the new distribution in extreme value analysis with a real data set.