An Upper Bound for the Expected Difference between Order Statistics

• Autores: Manuel Lopez, James Marengo
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 84, Nº. 5, 2011, págs. 365-368
• Idioma: inglés
• DOI: 10.4169/math.mag.84.5.365
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• Resumen

  • It is well known that the order statistics of a random sample from the uniform distribution on the interval [0, 1] have Beta distributions. In this paper we consider the order statistics of a random sample of n data points chosen from an arbitrary probability distribution on the interval [0, 1]. For integers k and l with 1 ?k ? l ? n we find an attainable upper bound for the expected difference between the order statistics Yl and Yk . This upper bound depends on the choice of k and l but does not depend on the distribution from which the data are obtained. We suggest a possible application of this result and we discuss some of its special cases.