Abstract
We investigated the relationship between the length x and the vocabulary y of texts within a sample of n texts. To this end, we tested several functions y = f(x,θ) by a parametric non-linear regression approach and use the residual sum of squares as a measure for the goodness of fit. It seems that the simple relationship y = A.x b with b ≃ 0.5 performs well (within the limited range of text lengths x in our samples). The residuals from the non-linear fit can serve as measures of vocabulary richness. This is demonstrated by a two-dimensional cluster plot for the scriptures of the New Testament. It was found that texts acknowledged as being members of the same group cluster together
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