This paper examines data from English, Swedish and German in order to find a theoretical distribution that describes the observed relation between word length and frequency. In Swedish and English, most word tokens consist of three letters only, while shorter or longer words occur less frequently. We found that the equation with the general form f exp ¼ a * L b * c L (a variant of the so-called gamma distribution) approximates the observed frequencies reasonably well. This formula incorporates both the fact that the number of possible words increases with word length, and the fact that longer words tend to be avoided, presumably because they are uneconomic. To our knowledge this formula has not been proposed to describe word frequency data. We examined frequency distributions of word length in Swedish and English, and explored different variants of the equation by systematically varying the a, b and c parameters. Subsequently, we also applied the formula to the frequency distribution of sentence length in English, and found an almost perfect fit for a corpus consisting of different text genres. Moreover, the data showed that the formula can be used to distinguish between different kinds of text genres.

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Numbers are used for exact and approximative estimations. The numbers used in approximative expressions are typically so-called round numbers, such as 10, 20, 25, 30, 40, 50, 100, 1,000, and such numbers are also very frequent in texts. This article presents evidence that some numbers are rounder than others and discusses how the roundness of a number can be derived from its contents of the base number of the numeral system of the culture. A formula for deriving the roundness of a number is suggested, and some evidence that intuitions about roundness vary between vigesimal and decimal cultures as predicted by the formula is given.