Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Characterization based on conditional expectations of adjacent order statistics:
A unified approach


Authors: M. Franco and J. M. Ruiz
Journal: Proc. Amer. Math. Soc. 127 (1999), 861-874
MSC (1991): Primary 62E10, 62G30, 60E05
DOI: https://doi.org/10.1090/S0002-9939-99-04913-8
MathSciNet review: 1610960
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show a unified approach to the problem of characterizing general distribution functions based on the conditional expectation between adjacent order statistics, $\xi (x)=E(h(X_{r,n})\mid X_{r+1,n}=x)$ or $\overline{\xi }(x)=E(h(X_{r+1,n})\mid X_{r,n}=x)$, where $h$ is a real, continuous and strictly monotonic function. We have the explicit expression of the distribution function $F$ from the above order mean function, $\xi $ and $\overline{\xi }$, and we give necessary and sufficient conditions so that any real function can be an order mean function. Our results generalize the results given for the discrete, absolutely continuous and continuous cases. Further, we show stability theorems for these characterizations.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 62E10, 62G30, 60E05

Retrieve articles in all journals with MSC (1991): 62E10, 62G30, 60E05


Additional Information

M. Franco
Affiliation: Departamento de Estadística e I.O., Universidad de Murcia, 30100 Murcia, Spain
Email: mfranco@fcu.um.es

J. M. Ruiz
Affiliation: Departamento de Estadística e I.O., Universidad de Murcia, 30100 Murcia, Spain
Email: jmruizgo@fcu.um.es

DOI: https://doi.org/10.1090/S0002-9939-99-04913-8
Keywords: Order statistics, $(n-r)$-out-of-$n$ system
Received by editor(s): June 5, 1997
Additional Notes: This work was partially supported by DGES (MEC), Grant PB96-1105.
Communicated by: Wei Y. Loh
Article copyright: © Copyright 1999 American Mathematical Society