THE VARIANCE AND THE RANGE OF IID RANDOM-VARIABLES

Chow and Teugels (1978) discussed the joint asymptotic behaviour, as n→∞, of the sum and the maximum of n i.i.d. random variables. Here it is noted that it is more natural to include also the minimum in the discussion, and that one can extend their argument to allow this; of course this means that the range can also be dealt with. Moreover the variance, like many U-statistics, can be approximated by a sum of transforms of the basic random variables, and similar methods can be used to study the joint asymptotic behaviour of, for example, the variance and the maximum and minimum. © 1990, Taylor & Francis Group, LLC. All rights reserved.