The Open Mathematics, Statistics and Probability Journal

2016, 7 : 36-44
Published online 2016 October 10. DOI: 10.2174/1876527001607010036
Publisher ID: TOSPJ-7-36

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

Ali A. Al-Shomrani, *

Address correspondence to this author at the Department of Statistics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah 21589, ; Tel: +966504379305; E-mail: email2aaalshomrani@yahoo.com

ABSTRACT

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.