Summary
Let X 1,X 2,… be independent with a common distribution function F(x) which has a finite mean, and let be the ordered values X 1, …,X n. The distribution of the n values EZ n1, …, EZ nn on the real line is studied for large n. In particular, it is shown that as n→∞, the corresponding distribution function converges to F(x) and any moment of that distribution converges to the corresponding moment of F(x) if the latter exists. The distribution of the values Ef(Z nm) for certain functions f(x) is also considered.
Work clone under the sponsorship of the Office of Naval Research.
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© 1994 Springer Science+Business Media New York
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Hoeffding, W. (1994). On the Distribution of the Expected Values of the Order Statistics. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_14
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DOI: https://doi.org/10.1007/978-1-4612-0865-5_14
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