The slashed Lomax distribution: new properties and Mellin-type statistical measures for inference

Area of Science:

• Statistics
• Probability Theory
• Survival Analysis

Background:

• Continuous distributions are crucial for modeling lifetime data, with the Slashed Lomax (SL) distribution gaining attention for its flexibility with heavy-tailed datasets.
• Existing statistical tools for assessing the goodness-of-fit of newly proposed continuous models, like the SL distribution, are limited.

Purpose of the Study:

• To develop novel goodness-of-fit measures for the Slashed Lomax distribution.
• To introduce a robust statistical methodology for evaluating model fit in survival analysis.
• To address the deficit in statistical tools for assessing flexible lifetime data models.

Main Methods:

• Derivation of the Mellin Transform (MT) for the SL distribution.
• Calculation of log-cumulants and construction of the log-cumulant diagram.
• Development of a test statistic combining Hotelling's T^2 and the multivariate Delta method for hypothesis testing on log-cumulants.

Main Results:

• The Mellin Transform was successfully derived for the SL distribution.
• New goodness-of-fit measures were constructed, considering both qualitative and quantitative aspects.
• Bootstrap experiments demonstrated the power of the proposed test and the performance of estimators.

Conclusions:

• The developed log-cumulant method and associated statistical tools are effective for evaluating the goodness-of-fit of the SL distribution.
• The methodology shows promise for assessing model fit in survival analysis using real-world datasets.
• The study contributes valuable statistical tools for the analysis of flexible lifetime data models.