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

MathSciNet review:
1610960

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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, or , where is a real, continuous and strictly monotonic function. We have the explicit expression of the distribution function from the above order mean function, and , 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.

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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