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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The Weibull distribution and its variants are widely used in reliability and survival analysis.
  • Existing distributions may lack flexibility for certain real-world datasets.
  • The inverse Weibull distribution provides an alternative but can be enhanced.

Purpose of the Study:

  • Introduce a novel transformed inverse Weibull distribution.
  • Analyze its statistical properties and parameter estimation methods.
  • Evaluate its practical applicability and fitting performance.

Main Methods:

  • Mathematical transformation of the inverse Weibull distribution.
  • Derivation and analysis of probability density, survival, and quantile functions.
  • Investigation of various entropy measures (Shannon, Rényi, Tsallis, Mathai-Haubold).
  • Parameter estimation using Maximum Likelihood Estimation (MLE) and Bayesian estimation.
  • Performance evaluation via Monte Carlo simulations.
  • Application to two real-world datasets.

Main Results:

  • The transformed inverse Weibull distribution possesses a flexible parameter structure.
  • Detailed characterization of its key statistical properties and entropy measures.
  • Comparative analysis of parameter estimation techniques.
  • Demonstrated superior goodness-of-fit compared to several established distributions (Weibull, generalized exponential, etc.).

Conclusions:

  • The transformed inverse Weibull distribution is a viable and effective statistical model.
  • It offers enhanced flexibility and fitting capabilities for practical data analysis.
  • The study validates its superiority over existing models in specific applications.