Plotting positions in extreme value analysis

Lasse Makkonen (Corresponding Author)

    Research output: Contribution to journalArticleScientificpeer-review

    135 Citations (Scopus)


    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.
    Original languageEnglish
    Pages (from-to)334-340
    Number of pages7
    JournalJournal of Applied Meteorology and Climatology
    Issue number2
    Publication statusPublished - 2006
    MoE publication typeA1 Journal article-refereed


    • extreme value analysis
    • plotting positions
    • return period
    • risk analysis
    • extreme events


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