(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:R2 --> 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.
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