We establish the equivalence of conditional unbiasedness and Lehmann's risk unbiasedness and a necessary and sufficient condition for the existence of such estimators. This condition brings out transparently the reason for the nonexistence of such estimators in most cases based on single stage...

Let X1,...,Xn be a random sample from an absolutely continuous distribution with non-negative support, and let Y1,...,Yn be mutually independent lifetimes with proportional hazard rates. Let also X(1)...X(n) and Y(1)...Y(n) be their associated order statistics. It is shown that the pair...

Let Rn be the range of a random sample X1,...,Xn of exponential random variables with hazard rate [lambda]. Let Sn be the range of another collection Y1,...,Yn of mutually independent exponential random variables with hazard rates [lambda]1,...,[lambda]n whose average is [lambda]. Finally, let r...

Recently, a new variability ordering, called right spread ordering or excess wealth ordering has been introduced. This new ordering is weaker than dispersive ordering. We show in this note that if X is less variable than Y in the sense of right spread ordering or convex ordering, then it implies...

Suppose X1,...Xn are independent random variables of continuous type with proportional hazard (or failure) rates. Let X(r) denote the rth order statistic and let I(r) = i if Xi = X(r). It is proved that Xi's are identically distributed if and only if X(r) and I(r) are independent for some r [set...

Let X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n denote the order statistics of a random sample X1,X2,...,Xn from a probability distribution with distribution function F. Similarly, let Y1:n[less-than-or-equals,...

Randles et al. (1980) and Davis and Quade (1978) independently proposed an asymptotically distribution-free test for testing symmetry about an unknown point. In this note, it has been shown that if X is convex ordered with respect to -- X, then the one-sided test is consistent, thus solving an...

First we consider the two-sample dispersion problem. Let X and Y be independent random variables of continuous type with distribution functions F and G, respectively, satisfying G(x) = F([sigma]x) for all x where [sigma] 0 and F(x) = 1 - F(- x), for all x. Let X1, X2 (Y1, Y2) be two independent...

An asymptotically distribution-free test is proposed and studied for testing the null hypothesis H0: Fdisp = G versus H1: Fdisp G, that is G-1([beta])-G-1([alpha])[greater-or-equal, slanted]F-1([beta])-F-1([alpha]) for 0[less-than-or-equals, slant][alpha][beta][less-than-or-equals, slant]1. The...