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Exact laws of large numbers for independent Pareto random variables
by Toshio Nakata

Vol. 12 No. 4 (2017) P.325~P.338
 DOI: https://doi.org/10.21915/BIMAS.2017403 10.21915/BIMAS.2017403

ABSTRACT

This article explores weighted laws of large numbers, namely $\it{exact}$ $\it{laws}$, for independent $\it{Pareto}$ distributions with infinite mean. It contains not only exact weak laws but also exact strong laws. Moreover, we give a simple example of the exact strong law applying the algorithm of Adler and Wittmann (1994).

KEYWORDS
Exact law of large numbers, Pareto distribution, infinite mean.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F05, 60F15

MILESTONES