Functional Form, Elasticity and Lexical Richness: Estimates and Implications

Traditionally, in estimating indexes of lexical richness, we must choose a mathematical formula on a priori grounds. Because this choice can have untoward consequences, we propose a different methodology. More specifically, we derive theoretically the indexes of lexical richness interest by introducing a new methodology, which is based on the elasticity of vocabulary (= V) with respect to text size (= N). The key consideration here is the method of specification of the elasticity. After the generation of the final Equation, regression can be used to produce estimates of indexes of lexical richness or to test hypotheses of interest. To the best of our knowledge, no one has published a rigorous proof where the mathematical formulas of indexes of lexical richness follow from the specification of the elasticity. Thus, the specification of the elasticity and the use of the theoretically derived functions to estimate the indexes of lexical richness is methodologically important in text analysis research. Since the indexes of lexical richness are the end products of such a methodology, they would seem to be a highly desirable object of study. In this paper, using a specification of elasticity, we have derived an index of lexical richness which includes, as special cases, the most widely known lexical indexes. One may ask whether these theoretical notions have any practical importance. For instance, does the specification of the elasticity produce appropriate indexes of lexical richness estimates? Apparently the answer is yes, as evidenced by the empirical results reported in this study. DOI: 10.4018/978-1-60960-786-9.ch005 Functional Form, Elasticity and Lexical Richness