### Abstract

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 language | English |
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Pages (from-to) | 334-340 |

Number of pages | 7 |

Journal | Journal of Applied Meteorology and Climatology |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

MoE publication type | A1 Journal article-refereed |

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### Keywords

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