Limit theorems for arrays of ratios of order statistics. (English) Zbl 1084.62015
Let \(\{{X_{nk},1\leq{k}\leq m_{n},n\geq1}\}\) be independent random variables with the Pareto distribution. Let \({X_{n(k)}}\) be the \(k^{th}\) largest order statistic from the \(n^{th}\) row of the array. Let, for \(j<i, R_{nij}=X_{n(j)}/X_{n(i)}\). The main aim of this paper is to present limit theorems involving weighted sums from the sequence \(\{R_{nij},\;n\geq1\}\). Thus, one can say that the author presents ”unusual” strong and weak laws of large numbers.
Reviewer: Zdzisław Rychlik (Lublin)
MSC:
62E20 | Asymptotic distribution theory in statistics |
60F15 | Strong limit theorems |
62G30 | Order statistics; empirical distribution functions |
60F05 | Central limit and other weak theorems |
60G50 | Sums of independent random variables; random walks |