Abstract
Two problems of extreme value theory are considered. Assessing the first one the importance is stressed of the direct evaluation of the exact distribution of the maximum \( \rlap{--} m_n \) of n independent identically distributed random values with a distribution function F(x). This evaluation is made in terms of the distribution denoted F n(x). Advantages of such an approach are compared with the classical method providing an asymptotic distribution of normalized maximum m n. Solving the second problem a threshold t, is derived that determines the upper half of the m n — distribution. An approximation of the distribution function F(x) can be facilitated if its range is restricted to x>t n.
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References
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© 2002 Springer Science+Business Media Dordrecht
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Pisarenko, V.F. (2002). On the Distribution of the Maximum of a Random Sample. In: Bolgov, M.V., Gottschalk, L., Krasovskaia, I., Moore, R.J. (eds) Hydrological Models for Environmental Management. NATO Science Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0470-1_2
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DOI: https://doi.org/10.1007/978-94-010-0470-1_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0911-2
Online ISBN: 978-94-010-0470-1
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