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Extreme values are the largest or the smallest observations in a sample; e.g., the sample minimum (the first order statistic) and the sample maximum (the n-th order statistic). Associated with extreme values are asymptotic *extreme value distributions.*
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Most probable value vs maximum of the distribution
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To make it easier for comprehension, we may consider the discrete case, where 'p(x) is maximum' refers to the event that takes place most, while 'Most probable value of x weighted over p(x).' (exp …