Bringing Closure to the Plotting Position Controversy

Abstract

In this article, it is explicitly demonstrated that the probability of non exceedance of the mth value in n order ranked events equals m/(n + 1). Consequently, the plotting position in the extreme value analysis should be considered not as an estimate, but to be equal to m/(n + 1), regardless of the parent distribution and the application. The many other suggested plotting formulas and numerical methods to determine them should thus be abandoned. The article is intended to mark the end of the century-long controversial discussion on the plotting positions.

Keywords:

• Cumulative distribution function
• Extreme value analysis
• Order ranking
• Plotting positions
• Probability paper

Mathematics Subject Classification:

• 62G30
• 62G32

Acknowledgments

Thanks are due to M. Pajari for continuous and fruitful discussions and comments on the manuscript. This work was funded by the Environmental Cluster Research Program, Ministry of Environment, Finland and Tekes.