Some asymptotic expansions of moments of order statistics

Peter Hall

Stochastic Processes and their Applications, 1978, vol. 7, issue 3, 265-275

Abstract: Series expansions of moments of order statistics are obtained from expansions of the inverse of the distribution function. They are valid for certain types of distributions with regularly varying tails. We show that the expansions converge quickly when the sample size is moderate to large, and we obtain bounds on the rate of convergence. The special case of the Cauchy distribution is treated in more detail.

Keywords: order; statistics; moments; asymptotic; expansions; Cauchy; distribution (search for similar items in EconPapers)
Date: 1978
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