4.1 Definition
Let us consider a random order m homogeneous Markov sequence X = X1,...,Xn on the finite alphabet  (cardinal k). If Ni is the random variable counting the number of occurrences (overlapping or renewal) of a given pattern in X1...Xi. We define the pattern statistic associated to any number Nobs ∈ ℕ of observations by
This way, a pattern has a positive statistic if it is seen more than expected, a negative statistic if seen less than expected and, in both cases, the corresponding p-value is given (in log scale) by the magnitude of the statistic.
The problem is: how to compute this statistic ?