For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past… (More)

Consider a sequence of independent random elements {Vn, n > in a real separable normed linear space (assumed to be a Banach space in most of the results), and sequences of constants {a,, n > and {ha,… (More)

Consider independent and identically distributed random variables {Xnk, 1 ≤ k ≤ m, n ≥ 1} from the Pareto distribution. We randomly select two adjacent order statistics from each row, Xn(i) and… (More)

This paper explores a Weighted Exact Weak Law, where the classical Weak Law fails and the corresponding Strong Law also fails. This type of result comes from the Fair Games problem and is associated… (More)

Herein we show a simple way to make the St. Petersburg Game fair for both Peter and Paul. By just considering the minimum of two simultaneous games we establish a way that could easily have been… (More)