Volume 6, Number 1 (March 2007)                   JIRSS 2007, 6(1): 47-60 | Back to browse issues page


XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Charalambides C A. On the Distribution and Moments of Record Values in Increasing Populations. JIRSS. 2007; 6 (1) :47-60
URL: http://jirss.irstat.ir/article-1-220-en.html

Abstract:   (4045 Views)
Consider a sequence of n independent observations from a population of increasing size αi, i = 1,2,... and an absolutely continuous initial distribution function. The distribution of the kth record value is represented as a countable mixture, with mixing the distribution of the kth record time and mixed the distribution of the nth order statistic. Precisely, the distribution function and (power) moments of the kth record value are expressed by series, with co- efficients being the signless generalized Stirling numbers of the first kind. Then, the probability density function and moments of the kth record value in a geometrically increasing population are expressed by q-series, with coefficients being the signless q-Stirling numbers of the first kind. In the case of a uniform distribution for the initial popu- lation, two equivalent q-series expressions of the jth (power) moment of the kth record value are derived. Also, the distribution function and the moments of the kth record value in a factorially increasing population are deduced.
Full-Text [PDF 146 kb]   (1375 Downloads)    
Subject: 60: Probability theory and stochastic processes
Received: 2013/08/21 | Accepted: 2015/09/12

Add your comments about this article : Your username or email:
Write the security code in the box

© 2015 All Rights Reserved | Journal of The Iranian Statistical Society