In this paper, we define different types of estimators for the distribution function, namely preliminary test (PT), shrinkage PT (SPT), Stein type (S), and Thompson shrinkage (TS) estimators based on lower record observations and their inter record times. Their asymptotic distributional bias and...

Given a scalar random variable Y and a random vector X defined on the same probability space, the conditional distribution of Y given X can be represented by either the conditional distribution function or the conditional quantile function. To these equivalent representations correspond two...

A class of nonparametric test statistics for several sample scale problem is proposed by considering extrema of subsamples of size c. The proposed class of statistics has the advantage of not requiring the several distribution functions to have a common median, but rather any common quantile of...

The main results imply that the probability P(Z∈A+θ) is Schur-concave/Schur-convex in (θ12,…,θk2) provided that the indicator function of a set A in Rk is so, respectively; here, θ=(θ1,…,θk)∈Rk and Z is a standard normal random vector in Rk. Moreover, it is shown that the...