Titlebook: Approximate Distributions of Order Statistics; With Applications to R.-D. Reiss Book 1989 Springer-Verlag New York Inc. 1989 Mathematica.Pa

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Inequalities and the Concept of Expansions bounds correspond to those for sums of independent r.v.’s. In Section 3.1 such bounds are established in the particular case of order statistics of i.i.d. random variables with common uniform d.f. on (0,1). This section also contains two applications to moments of order statistics.

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Approximations to Distributions of Central Order Statisticsributed. This result easily extends to the case of the joint distribution of a fixed number of central order statistics. In Section 4.1 we shall discuss some conditions which yield the weak and strong asymptotic normality of central order statistics.

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Extreme Value Modelsxtremes, whereas the nonparametric models contain actual distributions of sample extremes. The statistical inference within the nonparametric framework will be carried out by applying the parametric results.

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Distribution Functions, Densities, and Representationsion 1.3, the d.f. and density of a single order statistic. From this result and from the well-known fact that the spacings of exponential r.v.’s are independent (the proof is given in Section 1.6) we deduce the joint density of several order statistics in Section 1.4.

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Multivariate Order Statisticsatistics dealt with in Chapter 1. Our treatment of multivariate order statistics will not be as exhaustive as that in the univariate case because of the technical difficulties and the complicated formulae for d.f.’s and densities.

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Approximations to Distributions of Extremesriety of limiting d.f.’s the situation of the present chapter turns out to be more complex than that of the preceding chapter, where weak regularity conditions guarantee the asymptotic normality of the order statistics.

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