CLOSED-FORM EXPRESSIONS FOR THE MOMENTS OF THE BINOMIAL PROBABILITY DISTRIBUTION

被引：33
|
作者：
Knoblauch, Andreas [1 ]
机构：
[1] Honda Res Inst Europe, D-63073 Offenbach, Germany
来源：
SIAM JOURNAL ON APPLIED MATHEMATICS | 2008年 / 69卷 / 01期
关键词：
Stirling numbers; Pochhammer polynomial; neural associative memory; storage capacity; retrieval errors;
D O I：
10.1137/070700024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work develops closed-form expressions for the raw and central moments of the binomial probability distribution. For this I first derive a recursive formula for the raw moments from the moment generating function. Then it is shown that the recursion involved is essentially the same as for the Stirling numbers of the second kind. From this fact it is then possible to derive the closed formulae. Finally, I discuss an application of these formulae to the analysis of neural associative memory.
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页码：197 / 204
页数：8
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