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Moments of Cauchy Order Statistics via Riemann Zeta Functions

In: Statistical Theory and Applications

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  • P. C. Joshi
  • Sharmishtha Chakraborty

Abstract

We obtain exact expressions for the moments of single order statistics from a standard Cauchy distribution. These are expressed as linear combinations of Riemann zeta functions. Using these and numerical integration methods, means of order statistics from samples of sizes upto 25 have been tabulated. Second order moments and variances are then obtained by applying the recurrence relation given by Barnett (1966). They are also tabulated. Finally, we obtain expressions for product moments in terms of means of order statistics and Riemann zeta functions.

Suggested Citation

  • P. C. Joshi & Sharmishtha Chakraborty, 1996. "Moments of Cauchy Order Statistics via Riemann Zeta Functions," Springer Books, in: H. N. Nagaraja & Pranab Kumar Sen & Donald F. Morrison (ed.), Statistical Theory and Applications, chapter 11, pages 117-127, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3990-1_11
    DOI: 10.1007/978-1-4612-3990-1_11
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