  We present a large deviation property for the pattern statistics representing
the number of occurrences of a symbol in words of given length generated at
random according to a rational stochastic model. The result is obtained
assuming that in the model the overall weighted transition matrix is primitive.
In particular we obtain a rate function depending on the main eigenvalue and
eigenvectors of that matrix. Under rather mild conditions, we show that the
range of validity of our large deviation estimate can be extended to the
interval (0,1), which represents in our context the largest possible open
interval of validity of the property.
