Abstract
Abstract We give two different sets of bounds for the expected values of range, midrange and some other linear functions of order statistics from certain restricted families of distributions. The bounds are obtained by using Jensen's inequality on the expected values of some functions of the distribution function F which are convex (concave) strictly increasing. The bounds could be very useful, since exact values for the moments of these statistics, in general, are difficult to compute. The Weibull distribution is treated as a special case.
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