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Exact Distribution of the Occurrence Number for K-tuples Over an Alphabet of Non-Equal Probability Letters
Chan Zhou1, and Huimin Xie2
1Chu Kechen Honors College, Zhejiang University, Hangzhou 310027, China
zhouchan99@zju.edu.cn
2Department of Mathematics, Suzhou University, Suzhou 215006, China
szhmxie@pub.sz.jsinfo.net
Annals of Combinatorics 8 (4) p.499-506 December, 2004
AMS Subject Classification: 60C05, 05A15, 92B99
Abstract:
A nucleotide sequence can be considered as a realization of the non-equal-probability independently and identically distributed (niid) model. In this paper we derive the exact distribution of the occurrence number for each K-tuple with respect to the niid model by means of the Goulden-Jackson cluster method. An application of the probability function to get exact expectation curves [9] is presented, accompanied by comparison between the exact approach and the approximate solution.
Keywords: K-tuple, exact distribution, Goulden-Jackson cluster method, probability generating function, expectation curve of K-histogram

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