Abstract
The paper is to discuss the distribution theory of order statistics for finite sample sizes. Although the detailed exposition is on the independent and identically distributed case, some results, mainly in terms of inequalities, are also presented for dependent structures.
Growth properties of order statistics are discussed from two different points of view: an order statistic exceeding a certain level in terms of the sample size, and the distributional properties of future observations exceeding previously observed order statistics.
In the form of asymptotic results, laws of large numbers are discussed.
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Galambos, J. (1984). Introduction, Order Statistics, Exceedances. Laws of Large Numbers. In: de Oliveira, J.T. (eds) Statistical Extremes and Applications. NATO ASI Series, vol 131. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3069-3_2
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DOI: https://doi.org/10.1007/978-94-017-3069-3_2
Publisher Name: Springer, Dordrecht
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