LAWS OF LARGE NUMBERS FOR TWO TAILED PARETO RANDOM
VARIABLES
Abstract: We sample
random variables from a two tailed Pareto distribution. A two tailed Pareto distribution is a random variable
whose right tail is
and whose left tail is ,
where .
Next, we look at the largest of these random variables and establish various Weak and Strong
Laws that can be obtained with weighted sums of these random variables. The case of
is completely
different from .
2000 AMS Mathematics Subject Classification: Primary: 60F05, 60F15.
Key words and phrases: Almost sure convergence; weak law of large numbers; strong
law of large numbers.