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The Transmuted Marshall-Olkin Extended Lomax Distribution.

Renilma P DA Silva1,2, Audrey Helen M A Cysneiros1, Gauss M Cordeiro1

  • 1Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Estatística, Cidade Universitária, s/n, 50740-540 Recife, PE, Brazil.

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Researchers introduced a new transmuted Marshall-Olkin extended Lomax distribution. This flexible lifetime model demonstrates superior performance compared to existing distributions in real-world data analysis.

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Area of Science:

  • Statistics
  • Probability Distributions

Background:

  • The Marshall-Olkin extended Lomax distribution is a notable probability model.
  • Transmuted families of distributions are gaining research interest due to their flexibility.

Purpose of the Study:

  • To introduce the transmuted Marshall-Olkin extended Lomax distribution.
  • To investigate the mathematical properties and estimation methods for this new distribution.
  • To assess its performance and flexibility using real-world data.

Main Methods:

  • Generalization of the Marshall-Olkin extended Lomax distribution using the quadratic rank transmutation map.
  • Derivation and discussion of key properties: hazard rate, moments, characteristic function, and order statistics.
  • Maximum likelihood estimation procedure and simulation studies.
  • Empirical application to a real data set for performance evaluation.

Main Results:

  • The transmuted Marshall-Olkin extended Lomax distribution was successfully derived.
  • Key statistical properties were analyzed.
  • The maximum likelihood method was established for parameter estimation.
  • The new distribution demonstrated superior flexibility and performance compared to existing three- and four-parameter lifetime distributions on a real data set.

Conclusions:

  • The transmuted Marshall-Olkin extended Lomax distribution offers a flexible and effective tool for lifetime data analysis.
  • The proposed estimation method and empirical validation support its practical applicability.
  • This new distribution represents a valuable addition to the field of statistical modeling for reliability and survival analysis.