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Inverse power Maxwell distribution: statistical properties, estimation and application.

H S Al-Kzzaz1, M M E Abd El-Monsef1

  • 1Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

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Researchers developed a new inverse power Maxwell distribution for analyzing upside-down lifetime data. This flexible probability distribution demonstrated superior performance compared to existing models in real-world data analysis.

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • The Maxwell distribution is a foundational probability model.
  • Existing models may lack flexibility for certain lifetime data patterns.
  • There is a need for enhanced statistical distributions in reliability analysis.

Purpose of the Study:

  • Introduce a novel probability distribution: the inverse power Maxwell distribution.
  • Extend the capabilities of the Maxwell distribution for modeling specific data types.
  • Evaluate the statistical properties and estimation methods for the new distribution.

Main Methods:

  • Derivation of key statistical properties of the inverse power Maxwell distribution.
  • Application of five parameter estimation techniques (e.g., Maximum Likelihood Estimation).
  • Simulation studies to assess the performance of estimation methods.
  • Comparative analysis using two real-world datasets.

Main Results:

  • The inverse power Maxwell distribution was successfully formulated and its properties derived.
  • Simulation results indicated the viability of the proposed estimation methods.
  • The new distribution provided a significantly better fit to real datasets than several existing distributions.
  • The model's flexibility in capturing upside-down lifetime data was confirmed.

Conclusions:

  • The inverse power Maxwell distribution offers a valuable and flexible alternative for lifetime data analysis.
  • The proposed distribution outperforms established models in specific real-world applications.
  • This work contributes a new tool for statisticians and reliability engineers.