کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
415288 681197 2008 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Waiting time distribution of generalized later patterns
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Waiting time distribution of generalized later patterns
چکیده انگلیسی

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 naïve 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Statistics & Data Analysis - Volume 52, Issue 11, 15 July 2008, Pages 4879–4890
نویسندگان
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