Approximation by Penultimate Stable Laws
1997-09-04
Research Paper
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In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by a sequence of stable distributions with indices \\alpha_n \\to 2 than by a normal distribution. We discuss when this happens and how much the convergence rate can be improved by using penultimate approximations. Similar results are valid for other stable distributions.
Keywords
Automatically Extracted Terms
- lemma
- proof
- function
- nx =jtj
- f tx +f
- t 0 0
- cos x dx
- theorem
- convergence rate
- j log xj
- f anx =jtj
- distribution
- convergence
- t t 0
- n n 0
- n 0 0
- limt !1
- condition
- anx =jtj
- nx +f
