In real life phenomenon we experience largest observations (maximum extreme) or smallest observation (minimum extreme), such as “How tall should one design an embankment so that the sea reaches this level only once in 100 years?”; “What is the lowest value the Dow Jones Industrial Average can reach in the next three years?”; “How high a drug concentration in the bloodstream can go before causing toxicity?”, among others.
To characterize and understand the behavior of these extremes, we usually use probabilistic extreme value theory. Such theory deals with the stochastic behavior of the minimum and maximum of independent identically distributed random variables. Here, we shall give a brief introduction of the generalized extreme value family of probability distribution that fits the subject observations. This family of probability distribution function (pdf) consists of three famous classical pdfs, namely the Gumbel, the Frechet, and the Weibull.
Extreme value theory has been...
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Tsokos, C.P. (2011). Generalized Extreme Value Family of Probability Distributions. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_427
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