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Classical and Bayesian inference for the new four-parameter Lomax distribution with applications.

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A new statistical model, the New Alpha Power Transformed Power Lomax Distribution, was developed for analyzing lifetime data. This flexible distribution offers improved performance for reliability and survival analysis.

Keywords:
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Area of Science:

  • Statistics
  • Probability Distributions
  • Reliability Engineering

Background:

  • The Lomax distribution is a widely used probability model for analyzing lifetime data.
  • Existing Lomax distribution models may lack the flexibility to accurately capture complex lifetime data patterns.
  • New statistical distributions are needed to enhance the analysis of reliability and survival data.

Purpose of the Study:

  • To introduce a new flexible four-parameter Lomax distribution using an alpha power transformation technique.
  • To derive and investigate the mathematical properties of the proposed distribution.
  • To assess the performance of the new distribution in modeling real-world lifetime data.

Main Methods:

  • The New Alpha Power Transformed Power Lomax Distribution was mathematically derived.
  • Key properties including moments, quantile function, and mean residual life were obtained.
  • Parameter estimation was performed using Maximum Likelihood Estimation (MLE) and Bayesian estimation (Metropolis-Hastings).
  • Simulation studies evaluated the behavior of MLE estimators.
  • Model performance was demonstrated using two real-world lifetime data sets.

Main Results:

  • The mathematical properties of the New Alpha Power Transformed Power Lomax Distribution were successfully derived.
  • Simulation results indicated reliable performance of the Maximum Likelihood Estimators.
  • The proposed distribution demonstrated superior performance in fitting two real-world lifetime data sets compared to existing models.
  • Bayesian estimation provided approximate Bayes estimates for model parameters.

Conclusions:

  • The New Alpha Power Transformed Power Lomax Distribution is a valuable addition to the statistical toolkit for lifetime data analysis.
  • The proposed model offers enhanced flexibility and better interpretability for reliability and survival data.
  • Both Maximum Likelihood Estimation and Bayesian methods are effective for parameter estimation of the new distribution.