An attempt to measure the number of the total vocabulary of the individual by a statistical analysis of a sample of speech or writing - Kerr, David Sydney Mackay (My University, 2015)
The development of vocabulary tests is analysed and criticised. A new method of measurement is proposed based on an analysis of a sample of recorded speech or writing from an individual. The individual's vocabulary is defined as a fixed set of words having a probability of occurrence associated with each member of the set, and distributed according to a mathematical function, not necessarily specified. A theorem is derived which expresses the vocabulary contained In a text as a function of the frequency distribution and the length of text. Four forms of the text are quoted depending on whether the frequency distribution is taken as continuous or discrete and the text length as a natural or a real number,