Open AccessPlotting Positions in Extreme Value Analysis
Author(s) -
Lasse Makkonen
Publication year - 2006
Publication title -
journal of applied meteorology and climatology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.079
H-Index - 134
eISSN - 1558-8432
pISSN - 1558-8424
DOI - 10.1175/jam2349.1
Subject(s) - extreme value theory , statistics , return period , sample (material) , position (finance) , mathematics , rank (graph theory) , magnitude (astronomy) , econometrics , geography , economics , chemistry , physics , archaeology , finance , chromatography , combinatorics , astronomy , flood myth
Plotting order-ranked data is a standard technique that is used in estimating the probability of extreme weather events. Typically, observations, say, annual extremes of a period of N years, are ranked in order of magnitude and plotted on probability paper. Some statistical model is then fitted to the order-ranked data by which the return periods of specific extreme events are estimated. A key question in this method is as follows: What is the cumulative probability P that should be associated with the sample of rank m? This issue of the so-called plotting positions has been debated for almost a century, and a number of plotting rules and computational methods have been proposed. Here, it is shown that in estimating the return periods there is only one correct plotting position: P = m/(N + 1). This formula predicts much shorter return periods of extreme events than the other commonly used methods. Thus, many estimates of the weather-related risks should be reevaluated and the related building codes and other related regulations updated.