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Volume 7, Issue 1, Article 2 |
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An Inequality for the Asymmetry of Distributions and a Berry-Esseen Theorem for Random Summation
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Authors: |
Hendrik Kläver, Norbert Schmitz, |
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Keywords:
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Random number of i.i.d. random variables, Central limit theorem for random sums, Asymmetry of distributions, Berry-Esseen theorem for random sums. |
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Date Received:
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16/03/04 |
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Date Accepted:
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15/12/05 |
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Subject Codes: |
60E15, 60F05, 60G40.
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Editors: |
Sever S. Dragomir, |
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Abstract: |
We consider random numbers  of independent, identically distributed (i.i.d.) random variables  and their sums  . Whereas Blum, Hanson and Rosenblatt [3] proved a central limit theorem for such sums and Landers and Rogge [8] derived the corresponding approximation order, a Berry-Esseen type result seems to be missing. Using an inequality for the asymmetry of distributions, which seems to be of its own interest, we prove, under the assumption  (in an appropriate sense), a Berry-Esseen theorem for random summation.
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