Scaling of the minimum of iid random variables

Several areas in signal processing and communications rely on various tools in order statistics. Studying the scaling of the extreme values of iid random variables is of particular interest as it is sometimes only possible to make meaningful statements in the large number of variables case. This paper develops a new approach to finding the scaling of the minimum of iid variables by studying the behavior of the CDF and its derivatives at one point, or equivalently by studying the behavior of the characteristic function. The theory developed is used to study the scaling of several types of random variables and is confirmed by simulations.