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A new extended gumbel distribution: Properties and application.

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A new generalized Gumbel distribution family, based on the T-X paradigm, is introduced. This robust statistical model offers enhanced properties for risk assessment and data analysis.

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The Gumbel distribution is a fundamental tool in extreme value theory.
  • Generalizations of existing distributions are crucial for expanding their applicability.
  • The T-X paradigm offers a flexible framework for creating new probability distributions.

Purpose of the Study:

  • To propose a robust generalization of the Gumbel distribution using the T-X paradigm.
  • To derive and analyze the statistical properties of the new distribution family.
  • To demonstrate the model's utility through simulation and real-world data applications.

Main Methods:

  • Development of a new distribution family based on a linear combination of generalized exponential distributions.
  • Derivation of exact formulations for key statistical features: quantile function, moments, generating function, and order statistics.
  • Parameter estimation using the maximum likelihood method and skewness analysis including MacGillivray skewness.

Main Results:

  • A novel generalized Gumbel distribution family and three specific models were successfully formulated.
  • Comprehensive statistical properties were derived, providing a thorough understanding of the distributions.
  • The proposed model demonstrated superiority and authenticity in real-world data modeling and simulation assessments.

Conclusions:

  • The proposed generalized Gumbel distribution family offers a valuable and flexible extension to existing models.
  • The derived statistical properties and estimation methods facilitate practical applications.
  • The model's performance in risk indicator determination and data fitting highlights its potential in various fields.