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Power-Modified Kies-Exponential Distribution: Properties, Classical and Bayesian Inference with an Application to

Ahmed Z Afify1, Ahmed M Gemeay2, Nada M Alfaer3

  • 1Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt.

Entropy (Basel, Switzerland)
|July 27, 2022
PubMed
Summary
This summary is machine-generated.

A new power-modified Kies-exponential (PMKE) distribution is introduced for statistical modeling. This distribution and its parameter estimation methods are compared to existing models, showing potential for real-world data analysis.

Keywords:
Anderson–Darling estimationCramér–von Mises estimationexponential distributionmean residual lifepercentile estimationpower transformationrisk measures

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The exponential distribution is widely used but has limitations in modeling complex data.
  • There is a need for flexible statistical distributions with diverse hazard function shapes.

Purpose of the Study:

  • Introduce the novel power-modified Kies-exponential (PMKE) distribution.
  • Investigate the mathematical properties and hazard function behavior of the PMKE distribution.
  • Compare various classical and Bayesian parameter estimation methods for the PMKE distribution.

Main Methods:

  • Derivation of mathematical properties for the PMKE distribution.
  • Application of seven classical parameter estimation techniques.
  • Implementation of Bayesian estimation using square error, general entropy, and Linex loss functions.
  • Simulation studies to evaluate estimator performance.
  • Ranking of estimation methods based on simulation results.

Main Results:

  • The PMKE distribution exhibits flexible hazard function shapes (bathtub, increasing, decreasing).
  • Performance of classical and Bayesian estimators was evaluated through simulations.
  • A comparative analysis identified the most effective estimation approaches for PMKE parameters.
  • The PMKE distribution demonstrated utility in modeling a turbocharger dataset.

Conclusions:

  • The proposed PMKE distribution offers a valuable addition to the statistical modeling toolkit.
  • The study provides guidance on selecting optimal parameter estimation methods for the PMKE distribution.
  • The PMKE distribution shows promise for analyzing real-world data, outperforming existing exponential extensions.