International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 41-44, Pages 2325-2329
doi:10.1155/S0161171204401379

Complete convergence for arrays of minimal order statistics

Abstract

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 strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first moment of our order statistics is infinite.