An unbiased plotting position formula for the general extreme value distribution

Abstract

This paper introduces a new unbiased plotting position formula for the General Extreme Value distribution (GEV). The probability weighted moment (PWM) method is used to estimate the exact plotting positions. For practical application purposes, a simple formula representing a very reliable approximation to the exact plotting positions is proposed. It is found that the suggested formula provides a better agreement to the exact plotting positions than several existing formulas. Further, the proposed formula is conceptually more flexible and computationally more convenient because it can take explicity into account the skewness coefficient of the underlying distribution. It can be concluded that the plotting position formula developed in this study is the most appropriate for the GEV distribution. Finally, the development of probability papers for the GEV distribution for various skewness values is presented. Results of a numerical example have demonstrated the advantages related to the use of these special probability papers in engineering practice.