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A new cubic transmuted power-function distribution: Properties, inference, and applications.

Muhammad Ahsan-Ul-Haq1, Maha A Aldahlan2, Javeria Zafar1

  • 1College of Statistical & Actuarial Sciences, University of the Punjab, Lahore, Pakistan.

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|February 6, 2023
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Summary
This summary is machine-generated.

A novel cubic transmuted power distribution offers enhanced flexibility for modeling data. This new statistical model demonstrates superior performance compared to existing distributions, as confirmed by simulation and real-world data analysis.

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • Existing statistical distributions often lack the flexibility required for complex data patterns.
  • The cubic rank transformation offers a novel approach to developing new probability distributions.

Purpose of the Study:

  • To introduce a new three-parameter cubic transmuted power distribution.
  • To investigate the mathematical properties and estimation methods for the proposed distribution.
  • To assess the performance and flexibility of the new distribution against established models.

Main Methods:

  • Development of a new probability distribution using the cubic rank transformation.
  • Derivation of key mathematical properties: quantile function, moments, dispersion index, mean residual life, and order statistics.
  • Parameter estimation using five distinct methods, followed by a simulation study to evaluate estimator performance.
  • Application to a real-world dataset for practical validation.

Main Results:

  • The proposed cubic transmuted power distribution exhibits high flexibility in its density and hazard functions.
  • Simulation results indicate the behavior of derived estimators and identify the most effective estimation method.
  • The new distribution provides a better fit than several well-known existing distributions when applied to real data.

Conclusions:

  • The cubic transmuted power distribution is a flexible and effective addition to the statistical modeling toolkit.
  • The study validates the utility of the cubic rank transformation in creating novel probability distributions.
  • The proposed distribution offers a superior alternative for analyzing data where traditional models may be inadequate.