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June, 1971 Recurrence Relations for the Mixed Moments of Order Statistics
Prakash C. Joshi
Ann. Math. Statist. 42(3): 1096-1098 (June, 1971). DOI: 10.1214/aoms/1177693339


Let $X_1, X_2, \cdots, X_n$ be a random sample of size $n$ from a continuous distribution with cdf $P(x)$ and pdf $p(x)$. Let $X_{1:n} \leqq X_{2:n} \leqq \cdots \leqq X_{n:n}$ be the corresponding order statistics. Denote the first moment $E(X_{r:n})$ by $\mu_{r:n} (1 \leqq r \leqq n)$ and the mixed moment $E(X_{r:n}, X_{s:n})$ by $\mu_{r,s:n} (1 \leqq r \leqq s \leqq n)$. We assume that all these moments exist. Several recurrence relations between these moments are summarized by Govindarajulu [1]. In this note, we give a simple argument which generalizes some of the results given in [1]. These generalizations then lead to some modifications in the theorems given by Govindarajulu.


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Prakash C. Joshi. "Recurrence Relations for the Mixed Moments of Order Statistics." Ann. Math. Statist. 42 (3) 1096 - 1098, June, 1971.


Published: June, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0218.62047
Digital Object Identifier: 10.1214/aoms/1177693339

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 3 • June, 1971
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