We prove that Kendall’s Rank correlation matrix converges to the Marčenko Pastur law, under the assumption that observations are i.i.d random vectors X1, . . . , Xn with components that are independent and absolutely continuous with respect to the Lebesgue measure. This is the first result on the empirical spectral distribution of a multivariate U -statistic.

For q ∈ (0,1) fixed, we characterize the density functions f of absolutely continuous random variables X > 0 with finite expectation whose respective distribution functions satisfy the so-called (LBS) length-bias scaling property X L = qb X , where b X is a random variable having the distribution function b F (x) = (EX )−1 ∫ x 0 y f y d y. For an absolutely continuous random variable X > 0 with...

‎Independent random‎ ‎variables $Y_{1},ldots‎ ,‎Y_{n}$ belongs to the‎ ‎proportional reversed hazard rate (PRHR) model with‎ ‎proportionality parameters $lambda_1,...,lambda_n$‎, ‎if‎ ‎$Y_{k}sim G^{lambda _{k}}(x)$‎, ‎for $k=1,...,n$‎, ‎where $G$ is an‎ ‎absolutely continuous distribution function‎. ‎In this paper we compare‎ ‎the smallest order‎ ‎statistics‎, ‎the sample ranges and th...

We consider the functional equation f(t) = 1 b b?1 X =0 f t ? a for all t 2 IR; (F) where 0 < a < 1, b 2 IN n f1g and ?1 = 0 1 : : : b?1 = 1 are given parameters, f : IR ! IR is the unknown. We show that there is a unique bounded function f which solves (F) and satisses f(t) = 0 for t < ?1=(1 ? a), f(t) = 1 for t > 1=(1 ? a). This solution can be interpreted as the distribution function of a ce...