PMC:1647278 / 4034-4501 JSONTXT

{"project":"2_test","denotations":[{"id":"17044916-16722531-1696306","span":{"begin":107,"end":108},"obj":"16722531"},{"id":"17044916-9719638-1696307","span":{"begin":139,"end":140},"obj":"9719638"},{"id":"17044916-15840704-1696308","span":{"begin":141,"end":142},"obj":"15840704"},{"id":"17044916-15662195-1696309","span":{"begin":205,"end":207},"obj":"15662195"}],"text":"When π is known (and hence μ), several statistical methods are available to compute S: exact computations [1-4], Gaussian [5,6], binomial [7,8], compound Poisson [9-11] or large deviations approximations [12]. But in general, the parameter π is not available and must be estimated. Let us denote by N0 (resp. N1) the (overlap) frequencies of all words of size m (resp. m + 1) in the sequence Y = Y1 ... Yn, then the Maximum-Likelihood Estimator (MLE) of π is given by"}