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### Waiting time distribution of generalized later patterns

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Martina, Donald E. K. and Aston, John A. D..
(2008)
*Waiting time distribution of generalized later patterns.*
Computational Statistics & Data Analysis, Volume 52
(Number 11).
pp. 4879-4890.
ISSN 0167-9473

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1016/j.csda.2008.04.019

## Abstract

In this paper the concept of later waiting time distributions for patterns in multi-state trials is generalized to cover a collection of compound patterns. that must all be counted pattern-specific numbers of times, and a practical method is given to compute the generalized distribution. The solution given applies to overlapping counting and two types of non-overlapping counting, and the underlying sequences are assumed to be Markovian of a general order. Patterns are allowed to be weighted so that an occurrence is counted multiple times, and patterns may be completely included in longer patterns. Probabilities are computed through an auxiliary Markov chain. As the state space associated with the auxiliary chain can be quite large if its setup is handled in a naive fashion, an algorithm is given for generating a "minimal". state space that leaves out states that can never be reached. For the case of overlapping counting, a formula that relates probabilities for intersections of events to probabilities for unions of subsets of the events is also used, so that the distribution is also computed in terms of probabilities for competing patterns. A detailed example is given to illustrate the methodology. (C) 2008 Elsevier B.V. All rights reserved.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Statistics |

Library of Congress Subject Headings (LCSH): | Distribution (Probability theory), Bioinformatics |

Journal or Publication Title: | Computational Statistics & Data Analysis |

Publisher: | Elsevier Science Ltd |

ISSN: | 0167-9473 |

Official Date: | 15 July 2008 |

Volume: | Volume 52 |

Number: | Number 11 |

Number of Pages: | 12 |

Page Range: | pp. 4879-4890 |

Identification Number: | 10.1016/j.csda.2008.04.019 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

References: | Aston, J.A.D., Martin, D.E.K., 2005. Waiting time distributions of competing patterns in higher-order Markovian sequences. J. Appl. Probab. 42, 977–988. |

URI: | http://wrap.warwick.ac.uk/id/eprint/29590 |

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