Theoretical aspects and simulation with the application of a new two parameter distribution

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• Traditional statistical distributions often struggle to model complex real-world data.
• There is a continuous need for flexible and accurate probability distributions in various scientific fields.

Purpose of the Study:

• To introduce a new two-parameter distribution (NTPD) with unique characteristics.
• To derive key statistical properties of the NTPD.
• To evaluate the performance of parameter estimation methods for the NTPD.

Main Methods:

• Derivation of statistical properties: mode, reliability, hazard function, moments, moment generating function, Rényi entropy, fuzzy reliability, stochastic ordering, and quantile function.
• Parameter estimation using sixteen classical methods.
• Performance assessment via a comprehensive simulation study.
• Application to real-world datasets exhibiting high skewness and peakedness.

Main Results:

• Explicit derivation of numerous statistical properties for the NTPD.
• Comparative analysis of sixteen parameter estimation techniques.
• Demonstration of superior model fit for the NTPD across environmental, biomedical, and reliability datasets.
• NTPD outperformed established distributions like Lindley and exponentiated inverse Rayleigh.

Conclusions:

• The NTPD is a flexible and effective tool for modeling complex data.
• The study provides a robust framework for parameter estimation and performance evaluation.
• The NTPD offers a valuable alternative to existing distributions in applied statistics.