Exact laws for randomly selected order statistics
by
André Adler
Vol. 33 No. 1 (2005) P.1~P.19
ABSTRACT
Let $\{ X, X_{nj} , 1 \le j \le m, n \ge 1 \}$ be i.i.d. random variables with a generalized Pareto distribution where $EX = \infty$. We randomly select one of our order statistics
from $\{ X_{n(1)} , \ldots , X_{n(m)} \}$ with a predetermined set of probabilities. Calling that new random variable $Y_n$ we explore whether or not we can obtain constants an and $b_N$ so that $\sum_{n=1}^N a_nY_n / b_n$ converges in some sense to a nonzero constant, thus creating an
Exact Law of Large Numbers.
KEYWORDS
Strong law of large numbers, weak law of large numbers, exact laws, slow variation
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60F15, 60F05
MILESTONES
Received: 2003-08-07
Revised : 2003-11-27
Accepted:
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