Moments of Cauchy Order Statistics via Riemann Zeta Functions

P. C. Joshi and Sharmishtha Chakraborty

Chapter 11 in Statistical Theory and Applications, 1996, pp 117-127 from Springer

Abstract: 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.

Keywords: Bernoulli numbers and polynomials; Cauchy distribution; moments of order statistics; Riemann zeta function (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4612-3990-1_11

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