A novel extended inverse Weibull distribution: Statistical analysis and application.

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.