Distribution of Quantiles in Samples from a Bivariate Population
نویسنده
چکیده
Let F (x,y) be t he joint d istri but ion function of (X, y), possessing a probability density funct ion f(x,y). Let F I(X) and l>'2(Y) be the marginal distribut ion fun ctions of X and Y respectively. Let a be a quantile of FI (x) and f3 be a quantile of F2(y). A random sampl e (X k, Y k), k= 1, 2, ... , n, is drawn a nd t he values on each variate are ordered so that X:< X; a nd Y;< Y; if i < j. Let i and j be the greatest integers such t hat i /n::;' FI (a) and j /n::;' F2(f3), a nd let NI be the number of elements (X, Y) such t hat X<X; am! Y < Y. The joint distributio n of (M ,X;, Y;) is obtained and is shown to I'e asymptot icall y ;lOrlllal. Estimates a nd co nfidence limits on t he parameters of interest are also given.
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