Some results on conditional expectations of lower record values

Abstract

In this paper, we propose a measure for obtaining the expectation of time between two lower k-records under the condition that the greater one is given. Several properties of the proposed measure are derived. Some characterization results and stochastic comparisons based on the new measure are also provided.

Keywords:

• record statistics
• order statistics
• reversed hazard rate function
• characterization
• power function distribution

Acknowledgements

The authors would like to thank the Editor, an associate Editor and two anonymous referees for their valuable and constructive comments, which improved the presentation of the paper. We are grateful to the office of Graduate Studies of the University of Isfahan for their support. This work is supported in part by the ‘Ordered and Spacial Data Center of Excellence of Ferdowsi University of Mashhad’.