The power Lomax distribution with an application to bladder cancer data

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Bladder cancer remission times require flexible statistical models.
• Existing Lomax distribution extensions may not fully capture complex hazard rate behaviors.

Purpose of the Study:

• To propose and investigate the novel Power Lomax (POLO) distribution.
• To assess the POLO distribution's suitability for modeling bladder cancer remission times.
• To compare the POLO distribution with established Lomax distribution extensions.

Main Methods:

• Derivation of statistical and reliability properties for the POLO distribution.
• Application of method of moments and maximum likelihood estimation for parameter estimation.
• Simulation studies to evaluate the bias and mean square error of estimators.
• Real-world data analysis using bladder cancer remission times.

Main Results:

• The POLO distribution demonstrates capability for inverted bathtub and decreasing hazard rates.
• Maximum likelihood and method of moments estimators show reliable performance in simulations.
• The POLO distribution provides a superior fit compared to other Lomax extensions for bladder cancer data.

Conclusions:

• The proposed Power Lomax (POLO) distribution is a valuable and effective tool for analyzing bladder cancer remission data.
• POLO distribution offers improved modeling capabilities over existing Lomax distribution variants.
• This distribution has significant potential for applications in survival analysis and reliability engineering.