Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order

Agnieszka Goroncy () and Tomasz Rychlik ()

Metrika: International Journal for Theoretical and Applied Statistics, 2015, vol. 78, issue 2, 175-204

Abstract: Assume that $$X_1,\ldots , X_n$$ X 1 , … , X n are i.i.d. random variables with a common distribution function $$F$$ F which precedes a fixed distribution function $$W$$ W in the convex transform order. In particular, if $$W$$ W is either uniform or exponential distribution function, then $$F$$ F has increasing density and failure rate, respectively. We present sharp upper bounds on the expectations of single order statistics and spacings based on $$X_1,\ldots , X_n$$ X 1 , … , X n , expressed in terms of the population mean and standard deviation, for the family of all parent distributions preceding $$W$$ W in the convex transform order. We also characterize the distributions which attain the bounds, and specify the general results for the distributions with increasing density function. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Order statistics; Spacings; Optimal bound; Convex transform order; Increasing density; 60E15; 62G32 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00184-014-0495-7 (text/html)
Access to full text is restricted to subscribers.

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:spr:metrik:v:78:y:2015:i:2:p:175-204

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-014-0495-7

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().