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.
Citation
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