On the q-Weibull Distribution and Its Applications

Abstract

The q-Weibull distribution is a stretched model for Weibull distribution, obtained by introducing a new pathway parameter q, which facilitates a slow transition to the Weibull as q → 1. In this article, we make a detailed study of the properties of the q-Weibull distribution and we apply it to a data on cancer remission times for which this distribution is a better fit than Weibull. Results relating to reliability properties, estimation of parameters, and applications in stress-strength analysis are also obtained.

Keywords:

• Hazard rate function
• q-Weibull distribution
• Stress-strength analysis
• Survival function

Mathematics Subject Classification:

• Primary 62E15
• Secondary 62N05, 62-07

Acknowledgments

The authors are grateful to the reviewers and the Editor-in-Chief for the valuable suggestions which improved the presentation. The authors also thank the Department of Science & Technology, Government of India, New Delhi for financial assistance under project No: SR/S4/MS:287/05 which helped in the research leading to this article. This contribution is paper No. S20108 from Centre for Mathematical Sciences, Pala Campus, Kerala, India.