A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID-19 Data.

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The Lomax distribution is a widely used probability distribution.
• There is a continuous need for more flexible statistical distributions to model complex data.
• Recent trends in distribution theory focus on developing generalized and transmuted models.

Purpose of the Study:

• To introduce a new five-parameter transmuted generalization of the Lomax distribution (TGL).
• To derive key structural properties of the TGL, including moments and entropy.
• To demonstrate the applicability of the TGL using real-world COVID-19 data.

Main Methods:

• Derivation of closed-form expressions for moments, incomplete moments, quantile, and Rényi entropy.
• Estimation of parameters using Maximum Likelihood Estimation (MLE) for complete and Type-II censored data.
• Development of percentile bootstrap and bootstrap-t confidence intervals for parameter estimation.
• Monte Carlo simulations to evaluate point and interval estimation performance.

Main Results:

• The proposed TGL model exhibits greater flexibility compared to existing distributions.
• The study successfully derived various mathematical properties of the TGL.
• Parameter estimation methods (MLE, bootstrap) were developed and evaluated.
• The TGL model demonstrated its utility in analyzing COVID-19 datasets from France and the UK.

Conclusions:

• The new transmuted generalization of the Lomax distribution (TGL) is a valuable addition to statistical modeling tools.
• The TGL provides a more flexible alternative for analyzing various types of data.
• The TGL's effectiveness is confirmed by its application to real-world epidemiological data.