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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.
Anais Da Academia Brasileira De Ciencias
|October 28, 2020
Summary
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.
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.
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