A new cubic transmuted power-function distribution: Properties, inference, and applications.

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• Existing statistical distributions often lack the flexibility required for complex data patterns.
• The cubic rank transformation offers a novel approach to developing new probability distributions.

Purpose of the Study:

• To introduce a new three-parameter cubic transmuted power distribution.
• To investigate the mathematical properties and estimation methods for the proposed distribution.
• To assess the performance and flexibility of the new distribution against established models.

Main Methods:

• Development of a new probability distribution using the cubic rank transformation.
• Derivation of key mathematical properties: quantile function, moments, dispersion index, mean residual life, and order statistics.
• Parameter estimation using five distinct methods, followed by a simulation study to evaluate estimator performance.
• Application to a real-world dataset for practical validation.

Main Results:

• The proposed cubic transmuted power distribution exhibits high flexibility in its density and hazard functions.
• Simulation results indicate the behavior of derived estimators and identify the most effective estimation method.
• The new distribution provides a better fit than several well-known existing distributions when applied to real data.

Conclusions:

• The cubic transmuted power distribution is a flexible and effective addition to the statistical modeling toolkit.
• The study validates the utility of the cubic rank transformation in creating novel probability distributions.
• The proposed distribution offers a superior alternative for analyzing data where traditional models may be inadequate.