vocd-D (D Measure)
vocd-D, also called the D measure, is a length-robust index of lexical diversity developed by David Malvern and Brian Richards. Instead of reporting a single type-token ratio, it characterizes how a text's TTR falls as sample size grows and fits that empirical curve to a one-parameter probabilistic model; the fitted parameter D is the diversity score, with higher D meaning richer vocabulary. HD-D, introduced by McCarthy and Jarvis, is the mathematically exact, sampling-free counterpart that computes the same underlying quantity directly from the hypergeometric distribution.
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- Malvern, D., Richards, B., Chipere, N., & Durán, P. (2004). Lexical Diversity and Language Development: Quantification and Assessment. Palgrave Macmillan. · ISBN 9781403902313
- McCarthy, P. M., & Jarvis, S. (2007). vocd: A theoretical and empirical evaluation. Language Testing, 24(4), 459–488. · DOI 10.1177/0265532207080767
- McCarthy, P. M., & Jarvis, S. (2010). MTLD, vocd-D, and HD-D: A validation study of sophisticated approaches to lexical diversity assessment. Behavior Research Methods, 42(2), 381–392. · DOI 10.3758/BRM.42.2.381
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