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A relative frequency distribution is the proportion or fraction of times a value occurs in a data set. To find the relative frequencies, one can divide each frequency by the total number of data points in the sample. It is very similar to a regular frequency distribution, except that instead of reporting how many data values fall in a class, a relative frequency distribution reports the fraction of data values that fall in a class. These fractions or proportions are called relative frequencies...
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Updated: Jun 9, 2025

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Regional frequency analysis of extreme wind in Pakistan using robust estimation methods.

Ishfaq Ahmad1, Muhammad Salman1, Ibrahim Mufrah Almanjahie2

  • 1Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan.

Scientific Reports
|October 29, 2024
PubMed
Summary

This study estimates extreme wind speeds in Pakistan using regional frequency analysis. Generalized Extreme Value and Generalized Logistic distributions were identified as best fits for different regions, aiding in structural design.

Keywords:
Linear-momentsMonte Carlo simulationQuantile estimatesWind speed

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Area of Science:

  • Climatology and Meteorology
  • Statistical Hydrology
  • Extreme Value Theory Applications

Background:

  • Accurate quantile estimates of extreme wind speed are essential for structural design and risk assessment.
  • Regional Frequency Analysis (RFA) and Extreme Value Theory (EVT) are key methodologies for analyzing extreme events.
  • Wind speed data, measured at 10 meters, is critical for engineering and safety standards.

Purpose of the Study:

  • To perform Regional Frequency Analysis (RFA) of Annual Maximum Wind Speed (AMWS) in Pakistan's Khyber Pakhtunkhwa province.
  • To identify the most appropriate probability distributions for estimating regional quantiles of extreme wind speeds.
  • To provide reliable quantile estimates for codified structural designs and policy implications.

Main Methods:

  • Utilized L-moments for RFA of AMWS data from sixteen sites.
  • Employed the wards method to create two homogeneous regions, confirmed by heterogeneity tests.
  • Selected the best-fit probability distributions (GEV for Cluster-I, GLO for Cluster-II) using L-moments diagram and Z-statistics.

Main Results:

  • Two homogeneous regions were successfully constructed from the sixteen sites.
  • The Generalized Extreme Value (GEV) distribution was identified as the best fit for Cluster-I, and Generalized Logistic (GLO) for Cluster-II.
  • Robustness of the clusters was validated using relative bias (RB) and relative root mean square error (RRMSE).

Conclusions:

  • The study successfully applied RFA and EVT to estimate extreme wind speed quantiles in Khyber Pakhtunkhwa.
  • The identified GEV and GLO distributions provide a robust basis for regional quantile estimation.
  • The derived quantile estimates have direct applicability in structural design codes and policy development.