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Bridging Extremes: The Invertible Bimodal Gumbel Distribution.

Entropy (Basel, Switzerland)·2023
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A Revised Bimodal Generalized Extreme Value Distribution: Theory and Climate Data Application.

Cira E G Otiniano1, Mathews N S Lisboa1, Terezinha K A Ribeiro1

  • 1Statistics Department, University of Brasília, Brasília 70910-900, DF, Brazil.

Entropy (Basel, Switzerland)
|July 29, 2025
PubMed
Summary

A new bimodal generalized extreme value (BGEV) distribution with a location parameter enhances flexibility for modeling extreme events. This 2024 redefined model offers improved practical applications and statistical properties for climate data analysis.

Keywords:
bimodal GEV distributionheterogeneous dataproperties

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Area of Science:

  • Statistics
  • Extreme Value Theory
  • Climate Science

Background:

  • The original bimodal generalized extreme value (BGEV) distribution (2023) offered flexibility for bimodal extreme events but lacked a location parameter, complicating application.
  • The generalized extreme value (GEV) distribution is a standard but less flexible model for extreme events.

Purpose of the Study:

  • To investigate the properties of a redefined BGEV distribution incorporating a location parameter (2024).
  • To enhance the flexibility and practical applicability of BGEV models for extreme and heterogeneous data.
  • To provide a more robust statistical framework for analyzing complex extreme events.

Main Methods:

  • Derivation of explicit expressions for the probability density function (PDF) and hazard rate function.
  • Computation of the quantile function (QF) for the redefined BGEV distribution.
  • Establishment of the identifiability property and derivation of moments, moment-generating function (MGF), and entropy.

Main Results:

  • The redefined BGEV distribution with a location parameter demonstrates enhanced flexibility.
  • Explicit mathematical formulations for key distributional properties were successfully derived.
  • The identifiability of the new distribution class was confirmed.
  • Moments, MGF, and entropy were computed, providing a comprehensive statistical profile.

Conclusions:

  • The 2024 redefined BGEV distribution offers a more practical and flexible alternative to existing models for extreme value analysis.
  • The derived properties facilitate the application of this new distribution in various fields, including climate science.
  • The inclusion of a location parameter significantly improves the model's utility for real-world data with heterogeneous extreme events.