On the Probability Distribution of Typological Frequencies

Some language types are more frequent among the world’s languages than others, and the field of linguistic typology attempts to elucidate the reasons for such differences in type frequency. However, there is no consensus in that field about the stochastic processes that shape these frequencies, and there is thus likewise no agreement about the expected probability distribution of typological frequencies. This paper explains the problem and presents a first attempt to build a theory of typological probability purely based on processes of language change. 1 Probability distributions in typological research A central objective of the typological study of linguistic diversity is to explain why certain kinds of linguistic structures are much more frequently attested among the world’s languages than others. Unfortunately, such interpretations of empirically attested frequencies often rely on purely non-mathematic intuitions to judge whether observed frequencies are in any sense noteworthy or not. In the typological literature, this frequently leads to a tacit assumption that typological frequencies are evenly distributed, i.e. that a priori all language-types should be equally frequent, and any observed skewing of frequencies is thus in need of an explanation. Such an argumentation can be found, for example, in the widely read typological textbook by Comrie [2]: “In a representative sample of languages, if no universal were involved, i.e. if the distribution of types along some parameter were purely random, then we would expect each type to have roughly an equal number of representatives. To the extent that the actual distribution departs from this random distribution, the linguist is obliged to state and, if possible, account for this discrepancy” (p. 20) Various more sophisticated approaches to the interpretation of empirical frequencies often assume an underlyingly normal (or, more precisely, multinomial) distribution, as for example indicated by the regular use of χ statistics or Fisher’s exact test (e.g. in Cysouw [3]). Janssen et al. [6] and Maslova [12] explicitly discuss the problem of tacit assumptions of the underlying probability distributions as made in linguistic typology. As a practical solution to circumvent this problem for the assessment of statistical significance, Janssen et al. [6]