Confidence intervals for ratios of means applied to corpus-based word frequency classes

The words we choose when we communicate with one another convey meaning and information. In written or spoken language, we tend to employ a relatively small number of words repeatedly whereas a large number of words in the lexicon are seldom used. By considering a ratio of means of the most prevalent word in a body of texts (or corpus) compared to that of the word in question, one can quantify the prevalence of the word in question. Furthermore, the concept of word classes or grouping words having similar measures of prevalence enables the investigator to compare the words. Using a sample of texts having varying lengths from a corpus, the sample mean relative frequency of a word and the maximum likelihood estimator using the zero-inflated beta distribution serve as two measures of the prevalence of a word. We construct and then compare asymptotic confidence intervals involving ratios of means for a number of words in the British National Corpus, a 100 million-word collection of written and spoken language of a wide range of British English. We also examine the sample sizes required to meet specific objectives regarding word classes and ratios of means.