A well‐known problem in the domain of lexical statistics concerns the dependence of measures of lexical richness on the text size. To avoid this dependence, Large Number of Rare Event (LNRE) models have been developed, the parameters of which are, in theory, sample‐size invariant. In practice, however, the parameters of LNRE models may nevertheless reveal considerable dependence on the text size. We show that for LNRE models this dependence is a direct consequence of two factors: the non‐random use of words in texts on the one hand, and a theoretical lack of goodness‐of‐fit on the other hand. We describe how we can use this dependence to our advantage to enhance the interpolation and extrapolation accuracy of LNRE models. In addition, we outline methods for carrying out cross‐text comparisons using the empirical developmental profiles of LNRE parameters.
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