THE RELATION BETWEEN THE DICTIONARY DISTRIBUTION AND THE OCCURRENCE DISTRIBUTION OF WORD LENGTH AND ITS IMPORTANCE FOR THE STUDY OF QUANTITATIVE LINGUISTICS

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Abstract
One of the many unsolved problems of quantitative linguistics is the relation between the vocabulary and the occurrence distribution of specified linguistic forms, i.e. between the frequency distribution in the dictionary and that of occurrence in the spoken or written language. For different linguistic forms, such as phonemes, phoneme combinations (morphemes), word length (in terms of syllable, phoneme, letter number), the answer may conceivably be different. The present investigation deals with the characteristic of word length in terms of phoneme* and letter number per word, and arrives at the conclusion that the occurrence distribution can be regarded as a moment distribution of the vocabulary distribution. This will be shown to be a consequence of the log normality of word length distributions. To log normality of certain.linguistic distributions as an empirical fact Williams has drawn atention (1940, 1946). In this paper the hypothesis of log normality is extended to a set of related linguistic variables, viz. the distributions of both word occurrence and vocabulary according to word length in terms of the number of letters as well as phonemes. The comparison of these distributions as lognormal variates reveals the hypothesis of log normality as being of great value for the study of quantitative linguistics, practical and theoretical.

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