Proportional hazards model with quantile functions

ABSTRACT

Proportional Hazards Model (PHM) introduced by Cox (1972) is extensively studied in literature. In this paper, we study reliability properties of the PHM using quantile functions. Some special properties of the quantile function, which are not shared by distribution function are explored to study various properties of the PHM. We discuss ageing properties and stochastic orders for the PHM. The quantile-based dynamic cumulative Kullback-Leibler divergence of PHM is studied. Characterizations of some important quantile densities using PHM are also proved.

KEYWORDS:

• Characterization
• Cumulative Kullback-Leibler divergence
• Proportional Hazards model
• Quantile funtion
• Reliability measures
• Stochastic orders

MATHEMATICS SUBJECT CLASSIFICATION:

• 94A17
• 62N05

Acknowledgement

The authors wish to thank the referees and the editor for their constructive comments.

Funding

The second and third authors wish to thank the support of University Grants Commission, India, under Special Assistance Programme.