Probability Distributions of Grapheme Frequencies in Irish and Manx

Abstract

Drawing on the work of Grzybek and colleagues on Slavic and German, this study tests three hypotheses regarding the probability distribution of grapheme frequencies in Irish and Manx. First, is the 1-displaced negative hypergeometric distribution an appropriate theoretical distribution for grapheme frequencies in these languages? Second, does the language with the larger grapheme inventory exhibit larger values of the parameter K in this distribution? Third, are the parameters K and M of the 1-displaced negative hypergeometric distribution positively related in both languages? An analysis of 32 parallel texts (16 Irish + 16 Manx) suggests that the 1-displaced negative hypergeometric distribution is an appropriate model for both languages and that the parameters K and M are positively related. However, the analysis does not support the hypothesis that the language with the larger grapheme inventory also has higher values of K. Further work needs to clarify how far this latter finding extends beyond this sample of Irish and Manx.