Some Characterization and Relations Based on K-th Lower Record Values

Ali A. Al-Shomrani*
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

© Ali A.Al-Shomrani; Licensee Bentham Open

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (, which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

Correspondence: Address correspondence to this author at the Department of Statistics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, Saudi Arabia; Tel: +966504379305; E-mail:


In this paper, we obtain certain expressions and recurrence relations for two general classes of distributions based on some conditional expectations of k-th lower record values. We consider the necessary and sufficient conditions such that these conditional expectations hold for some distribution functions. Furthermore, an expression of conditional expectation of other general class of distributions through truncated moments of some random variable is considered. Some distributions as examples of these general classes are shown in Tables 1 and 2 accordingly.

Keywords: Characterization, Conditional expectation, Order statistics, Records values.