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CHARACTERIZATIONS BASED ON

CONDITIONAL EXPECTATIONS OF

THE DOUBLED TRUNCATED DISTRIBUTION

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J. M. RUIZ AND J. NAVARRO

*Departamento de Matemática Aplicada y Estadística,*

Universidad de Murcia, 30100 Murcia, Spain
(Received February 28, 1994; revised September 21, 1995)

**Abstract.**
The expression of the continuous
distribution function *F*(*x*) is obtained whenever *m*(*x*,
*y*) = *E*(*X* | *x* __<__ *X* __<__ *y*) is known. Moreover, we obtain
the necessary and sufficient conditions so that any
function *m*:R^{2} --> R is the conditional expectation
*E*(*X* | *x* __<__ *X* __<__ *y*) of a random variable *X* with
continuous distribution function. Furthermore, we
relate *m*(*x*, *y*) to order statistics.

*Key words and phrases*:
Characterizations,
doubled truncated distribution, conditional
expectations, mean residual life, order statistics.

**Source**
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