Some results on quantile-based Shannon doubly truncated entropy

ABSTRACT

Sunoj et al. [(2009). Characterization of life distributions using conditional expectations of doubly (Intervel)truncated random variables. Communications in Statistics – Theory and Methods, 38(9), 1441–1452] introduced the concept of Shannon doubly truncated entropy in the literature. Quantile functions are equivalent alternatives to distribution functions in modelling and analysis of statistical data. In this paper, we introduce quantile version of Shannon interval entropy for doubly truncated random variable and investigate it for various types of univariate distribution functions. We have characterised certain specific lifetime distributions using the measure proposed. Also we discuss one fascinating practical example based on the quantile data analysis.

KEYWORDS:

• Quantile function
• interval entropy
• geometric vitality function
• characterisation

Acknowledgments

The authors would like to express their gratitude to the reviewers and the editor-in-chief for their valuable comments, which have considerably improved the earlier version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author wishes to acknowledge the Science and Engineering Research Board (SERB), Government of India, for the financial assistance (Ref. No. ECR/2017/001987) for carrying out this research work.

Notes on contributors

Vikas Kumar

Vikas Kumar has obtained his M.Sc and M.Phil degree in Applied Mathematics from IIT Roorkee and ISM University, Dhanbad in 2005 and 2007 respectively. He received the Ph.D. degree in Mathematics from University of Delhi, Delhi. Currently, he is a Assistant Professor in Mathematics, UIET, M. D. University, Rohtak, India. His research interests are information theory and its applications and mathematical modeling. He has published research articles in reputed international journals of Mathematics and Statistical sciences.

Gulshan Taneja

Dr. Gulshan Taneja is working as Professor in Mathematics at M. D. University, Rohtak. He has vast experience of about 25 years of teaching in mathematics and statistics both at UG and PG levels. Dr. Taneja has published more than sixty research papers in the field of Information Theory & Reliability Theory in journals of international repute and is a member of various national and international societies.

Samsher Chhoker

Samsher Chokker has obtained his M.Sc and M.Phil degree in Mathematics from M. D. University, Rohtak in 2015 and 2017 respectively. He pursuing his Ph.D. degree in Mathematics from M. D. University, Rohtak . Currently, he is a Assistant Professor in Mathematics, Government PG Nehru College Jhajjar, India. His research interests are information theory and and mathematical modeling.