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June, 1964 Asymptotic Distribution of Distances Between Order Statistics from Bivariate Populations
O. P. Srivastava, W. L. Harkness, J. B. Bartoo
Ann. Math. Statist. 35(2): 748-754 (June, 1964). DOI: 10.1214/aoms/1177703573

Abstract

The exact and limiting distribution of quantiles in the univariate case is well known. Mood [3] investigated the joint distribution of medians in samples from a multivariate population, showing that their distribution is asymptotically multivariate normal. Recently Siddiqui [4] considered the joint distribution of two quantiles and an auxiliary statistic and showed that asymptotically their joint distribution is trivariate normal. Further, he showed the "distances" $X'_{i+l} - X'_i - X'_{i-h}$, ($l$ and $h$ fixed positive integers) between quantiles in the univariate case, when appropriately normalized are asymptotically independently distributed as Chi square r.v.'s with $2l$ and $2h$ d.f. respectively. In this paper the joint distribution of several quantiles from a bivariate population is obtained and it is shown that the distances between quantiles in the separate component populations are independent asymptotically.

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O. P. Srivastava. W. L. Harkness. J. B. Bartoo. "Asymptotic Distribution of Distances Between Order Statistics from Bivariate Populations." Ann. Math. Statist. 35 (2) 748 - 754, June, 1964. https://doi.org/10.1214/aoms/1177703573

Information

Published: June, 1964
First available in Project Euclid: 27 April 2007

zbMATH: 0127.36001
MathSciNet: MR161410
Digital Object Identifier: 10.1214/aoms/1177703573

Rights: Copyright © 1964 Institute of Mathematical Statistics

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Vol.35 • No. 2 • June, 1964
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