Waiting time distribution of generalized later patterns

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. The 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 na

• Type: Journal
• Year: 2008
• Where: CSDA
• Authors: Donald E. K. Martin, John A. D. Aston
• Keywords: Compound Patterns, CSDA 2008, Probabilities, State Space