Useful inequalities for the longest run distribution (Q1970812)
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scientific article; zbMATH DE number 1420524
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Useful inequalities for the longest run distribution |
scientific article; zbMATH DE number 1420524 |
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Useful inequalities for the longest run distribution (English)
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21 March 2000
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The author proves a simple and explicit lower bound for the probability that the longest success run in a sequence of \(n\) Bernoulli trials is less than a given length \(k\). The arguments used are analytic and combinatorial in nature. The lower bound is usually better than those obtained using compound Poisson approximation and Stein's method. See also \textit{S. Yu. Novak} [Theory Probab. Appl. 39, No. 4, 593-603 (1994); translation from Teor. Veroyatn. Primen. 39, No. 4, 731-742 (1994; Zbl 0847.60016)].
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longest success run
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Bernoulli trials
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compound Poisson approximation
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Stein's method
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