The Sampling Distribution of the Ratio of Two Ranges from Independent Samples
Richard F. Link · The Annals of Mathematical Statistics · 1950
Let us consider a sample of n ordered observations *(x < x2 < < x) drawn from a population with variance o2. Let w = (xn xl)/o. Let us consider the joint sampling distribution of w, and w2 for two samples, not necessarily the same size, drawn from populations with the same variance. If the two samples were drawn independently, then the joint sampling distributions of w, and w2 may be written as the product of the sampling distributions of w, and w2 . If we make the change of variable r = W11W2, W2 = w, and if w is integrated over its range of definition, the cumulative distribution of the ratio of two ranges remains. This may be written as