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Convergence theorems for the lengths of consecutive successes of Markov Bernoulli sequences

Part of: Distribution theory

Published online by Cambridge University Press:  14 July 2016

Y. H. Wang ,
Hsiao-Fen Chang  and
Shun-Yi Chen
Y. H. Wang*
Affiliation:
Tunghai University
Hsiao-Fen Chang*
Affiliation:
Tamkang University
Shun-Yi Chen*
Affiliation:
Tamkang University
*
∗Postal address: Department of Statistics, Tunghai University, Taichung, Taiwan, 407. Email address: [email protected]
∗∗Postal address: Department of Mathematics, Tamkang University, Taipei, Taiwan, 100
∗∗Postal address: Department of Mathematics, Tamkang University, Taipei, Taiwan, 100
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Abstract

The limiting distributions of the sums of the lengths of four different kinds of runs of consecutive successes of Markov Bernoulli sequences are derived. It is shown that the limits are convolutions of several distributions involving the Bernoulli, the geometric and the Poisson or compound Poisson distributions.

Keywords

Limit theoremPoisson limitconsecutive successes of length ksum of random variablesreliability

MSC classification

Primary: 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 741 - 749
Copyright
Copyright © Applied Probability Trust 2003 

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