International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 44, Pages 2325-2329

Complete convergence for arrays of minimal order statistics

André Adler

Department of Mathematics, Illinois Institute of Technology, Chicago 60616, IL, USA

Received 26 January 2004

Copyright © 2004 André Adler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.