Distribution of the Maximum of Independent Identically-distributed Variables
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چکیده
Many engineering applications require the calculation of the distribution of the maximum of a number n of indendent, identically distributed (iid) variables. A typical situation is the design of a system for the “n-year demand” when the maximum demands in different years are iid (design of a dam for the n-year flood, design of an offshore platform for the n-year wave, design of a building for the n-year wind, etc.). In some cases, for example the design of buildings against earthquake loads, using the year as the basic unit of time makes little sense, since earthquake occurrences do not have a yearly cycle (floods, winds, and sea-states do). Rather, earthquakes may be viewed as occurring at random times, say according to a Poisson process and maximization of the quantity of interest (for example earthquake magnitude or the induced monetary loss) should be done over the random number of earthquakes in a time period of duration T. Accordingly, we consider below maximum problems of two types:
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