Two new defective distributions based on the Marshall-Olkin extension

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Survival data frequently includes immune elements, often leading to a fraction of patients experiencing a cure.
• Standard mixture models are commonly employed to analyze such data.
• An alternative modeling approach is needed to address the complexities of these survival data.

Purpose of the Study:

• To introduce and explore defective distributions as an alternative to standard mixture models for survival data with immune elements.
• To generalize existing defective distributions using the Marshall-Olkin class.
• To demonstrate the application of these new distributions with real-world data.

Main Methods:

• Utilized defective distributions, characterized by density functions integrating to less than 1.
• Employed the Marshall-Olkin class of distributions to generalize two existing defective distributions.
• Developed two novel defective distributions.

Main Results:

• Successfully generalized two defective distributions using the Marshall-Olkin framework.
• Generated two new defective distributions for survival data analysis.
• Illustrated the practical application of these distributions through three real data set analyses.

Conclusions:

• Defective distributions offer a viable alternative for modeling survival data with immune elements.
• The proposed generalized defective distributions provide enhanced flexibility in survival analysis.
• The application to real data sets confirms the utility of this novel approach.