Frechet-power function distribution:Theory, properties and applications

Area of Science:

• Statistics
• Probability Theory
• Data Modeling

Background:

• Existing bounded lifetime models often lack flexibility.
• Complex data features like skewness and heavy tails are common.
• There is a need for versatile models for bounded data.

Purpose of the Study:

• To introduce the novel Fréchet-Power Function (FPF) distribution.
• To combine bounded support with heavy-tailed flexibility.
• To provide a versatile tool for bounded lifetime data analysis.

Main Methods:

• Derivation of probability density, cumulative distribution, and quantile functions.
• Analysis of statistical properties including moments and hazard rates.
• Parameter estimation via maximum likelihood estimation (MLE).
• Performance assessment using bootstrap and simulation techniques.

Main Results:

• The FPF distribution successfully models skewness, heavy tails, and diverse hazard rates.
• Explicit mathematical forms and properties of the FPF are derived.
• Maximum likelihood estimation and simulation studies validate estimator performance.
• Empirical applications demonstrate superior goodness-of-fit and flexibility over traditional models.

Conclusions:

• The Fréchet-Power Function (FPF) distribution is a powerful and flexible new model.
• It offers enhanced accuracy and interpretability for bounded lifetime data.
• The FPF distribution is applicable across survival, reliability, and environmental sciences.