Alpha-Power Pareto distribution: Its properties and applications

Area of Science:

• Statistics
• Probability Distributions
• Mathematical Modeling

Background:

• Standard statistical distributions are often extended by incorporating additional parameters to enhance their flexibility and applicability.
• The Pareto distribution is a widely used probability distribution in various fields, but its standard form may lack the necessary adaptability for certain datasets.

Purpose of the Study:

• To introduce a new flexible probability distribution, the Alpha-Power Pareto distribution, by adding an extra parameter to the standard Pareto model.
• To investigate the theoretical properties and practical utility of the proposed Alpha-Power Pareto distribution.

Main Methods:

• Derivation of key statistical properties including the moment generating function, mode, quantiles, and entropies.
• Calculation of mean residual life function, stochastic orders, and order statistics for the new distribution.
• Parameter estimation using the maximum likelihood estimation (MLE) technique and validation on two real-world datasets.

Main Results:

• The study successfully derived various mathematical and statistical properties of the Alpha-Power Pareto distribution.
• Parameter estimation was performed effectively using the maximum likelihood estimation method.
• Empirical analysis using two real datasets indicated that the Alpha-Power Pareto distribution provides a better fit compared to other Pareto distribution variants.

Conclusions:

• The proposed Alpha-Power Pareto distribution is a valuable addition to the family of statistical distributions.
• The enhanced flexibility of the Alpha-Power Pareto distribution makes it suitable for modeling complex real-world phenomena.
• The distribution's superior performance, as evidenced by model selection criteria, suggests its potential for broader application in statistical modeling and data analysis.