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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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Approximate Sufficiency of Sparse Order StatisticsThis chapter starts with an introduction to “comparison of statistical models” where in addition to Section 9.1 we also make use of Markov kernels.
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https://doi.org/10.1007/978-3-642-78687-7ion 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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https://doi.org/10.1007/978-3-531-19022-8 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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,Führung zur Verhaltensänderung,riety 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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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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