Abstract
Suppose X 1,… X n are independent random variables of continuous type with proportional hazard (or failure) rates. Let X ( r) denote the rth order statistic and let I ( r) = i if X i = X ( r) . It is proved that X i 's are identically distributed if and only if X ( r) and I ( r) are independent for some r ∈ {2,…, n}. The second characterization is in terms of order statistics from subsamples.
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