The Annals of Mathematical Statistics

Recurrence Relations Between the PDF's of Order Statistics, and Some Applications

K. S. Srikantan

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Abstract

In this paper we obtain a recurrence relation between the pdf's (probability density functions) of order statistics. This relation is then extended to their cdf's (cumulative distribution functions) and to the expected values of a given function of each order statistic and a function of pairs of them. The interrelation between these results and other known formulas is shown. The application of the results to the preparation of tables of cdf's, expected values, variances, etc., of order statistics is indicated, and the numerical errors propagated in such computations analysed. Finally, an illustration is given. It is hoped that the unified approach presented here will provide greater insight and flexibility to procedures of numerical evaluation of expected values, etc., of order statistics.

Article information

Source
Ann. Math. Statist., Volume 33, Number 1 (1962), 169-177.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704721

Digital Object Identifier
doi:10.1214/aoms/1177704721

Mathematical Reviews number (MathSciNet)
MR137237

Zentralblatt MATH identifier
0102.35601

JSTOR
links.jstor.org

Citation

Srikantan, K. S. Recurrence Relations Between the PDF's of Order Statistics, and Some Applications. Ann. Math. Statist. 33 (1962), no. 1, 169--177. doi:10.1214/aoms/1177704721. https://projecteuclid.org/euclid.aoms/1177704721


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