Let F(x1,...,xk) and G(x1,...,xk)=FX1(x1)...FXk(xk), where FXi(xi), 1[less-than-or-equals, slant]i[less-than-or-equals, slant]k, are the one-dimensional marginal distributions of F, be two distribution functions on . Here, we obtain explicit bounds for the Lévy-Prohorov distance between F and G...

Shanbag gave a characterization of the exponential and geometric distribution in terms of conditional expectations. Recently, Kotlarski generalized his method to obtain some properties of univariate probability distributions through conditional expectations. A property of bivariate distributions...

The asymptotic properties of the least squares estimator are derived for a nonregular nonlinear model via the study of weak convergence of the least squares process. This approach was adapted earlier by the author in the smooth case. The model discussed here is not amenable to analysis via the...

[Bobkov and Houdre (1997] proved that if [xi], [eta] and [zeta] are independent standard exponential random variables, then for any two absolutely continuous functions f and g such that Ef([xi])2[infinity] and Eg([xi])2[infinity], the equality Cov(f([xi]),g([xi]))=Ef'([xi]+[eta])g'([xi]+[zeta])...

A new concept of rth order strong mixing for sub [sigma]-algebras of a probability space is introduced and a bound for the rth order joint cumulant is obtained under a two-part dependence assumption, which includes the case of rth order strong mixing, generalizing the work of Bradley [(1996)...