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The development and implementation of odd-exponential-ailamujia distribution in python: properties and application in

Tmader Alballa1, Qasim Ramzan2,3, Muhammad Amin4

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This summary is machine-generated.

A new Odd-Exponential-Ailamujia (OEA) distribution offers flexible lifetime data modeling for reliability and survival analysis. It accurately fits complex failure patterns, outperforming existing models in real-world applications.

Keywords:
Ailamujia distributionParameter estimationPython implementationReliability analysisStatistical modelT-X family

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • Traditional lifetime distributions often lack the flexibility to model complex failure patterns.
  • The T-X family of distributions provides a framework for creating more adaptable statistical models.

Purpose of the Study:

  • Introduce the novel Odd-Exponential-Ailamujia (OEA) distribution.
  • Enhance flexibility in modeling complex lifetime data.
  • Provide a robust tool for reliability engineering and survival analysis.

Main Methods:

  • Derived key statistical properties (moments, MGF, characteristic function, etc.) using binomial and Taylor series expansions.
  • Transformed intractable integrals into computable forms for precise distributional approximation.
  • Analyzed the hazard rate function's behavior (increasing, decreasing, unimodal) based on parameters.

Main Results:

  • The OEA distribution demonstrated superior fit to aircraft windshield failure data compared to competing models.
  • Goodness-of-fit tests, reliability plots, and heatmaps confirmed the model's effectiveness.
  • Parameter analysis revealed correlations and controlled hazard rate shapes.

Conclusions:

  • The OEA distribution is a versatile and robust tool for reliability engineering and survival modeling.
  • It effectively captures real-world failure dynamics and probabilistic forecasting.
  • Efficient Python implementation supports scalable inference for practical applications.