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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 28, Fasc. 1,
pages 121 - 128
 

LAWS OF LARGE NUMBERS FOR TWO TAILED PARETO RANDOM VARIABLES

André Adler

Abstract: We sample $m$ random variables from a two tailed Pareto distribution. A two tailed Pareto distribution is a random variable whose right tail is $px^(-2)$ and whose left tail is $qx^(-2)$, where $p+q=1$. 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 $m=1$ is completely different from $m>1$.

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.

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