Abstract
Let \(\mathbb{A} = (A_i)_{1\leq i\leq n}\) be a sequence of letters taken in a finite alphabet Θ. Let \(s : \Theta \rightarrow \mathbb{Z}\) be a scoring function and \(\mathbb{X} = (X_i)_{1\leq i\leq n}\) the corresponding score sequence where X i = s(A i ). The local score is defined as follows: \(H_n=\max_{1\leq i\leq j\leq n}\sum_{k=i}^{j}X_k\). We provide the exact distribution of the local score in random sequences in several models. We will first consider a Markov model on the score sequence \(\mathbb{X}\), and then on the letter sequence \(\mathbb{A}\). The exact P-value of the local score obtained with both models are compared thanks to several datasets. They are also compared with previous results using the independent model.
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Hassenforder, C., Mercier, S. Exact Distribution of the Local Score for Markovian Sequences. AISM 59, 741–755 (2007). https://doi.org/10.1007/s10463-006-0064-6
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DOI: https://doi.org/10.1007/s10463-006-0064-6