On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach

Ahmad Reza Soltani and Rasool Roozegar

Statistics & Probability Letters, 2012, vol. 82, issue 5, 1012-1020

Abstract: In this article we employ certain techniques in divided differences to relate the generalized Stieltjes transform of the distribution of a randomly weighted average of independent random variables X1,…,Xm to the generalized Stieltjes transforms of the distribution functions F1,…,Fm; Xi∼Fi,i=1,…,m. The random weights are assumed to be cuts of [0,1] by m−1 ordered statistics of independent and identically uniformly distributed random variables U1,…,Un on [0,1]; m≤n. Soltani and Homei (2009) treated the case m=n using the Schwartz distribution theory. We identified fairly large classes of randomly weighted average distributions by their generalized Stieltjes transforms; in particular including the uniform, Wigner and certain power semicircle distributions.

Keywords: Randomly weighted average; Generalized Stieltjes transform; Stieltjes transform; Divided differences (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715212000545
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:82:y:2012:i:5:p:1012-1020

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2012.02.007

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().