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On the measure and the estimation of evenness and diversity

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  • Ginebra, Josep
  • Puig, Xavier

Abstract

Modelling word or species frequency count data through zero truncated Poisson mixture models allows one to interpret the model mixing distribution as the distribution of the word or species frequencies of the vocabulary or population. As a consequence, estimates of their mixing density can be used as a fingerprint of the style of the author in his texts or of the ecosystem in its samples. Definitions of measure of the evenness and of measure of the diversity within a vocabulary or population are given, and the novelty of these definitions is explained. It is then proposed that the measures of the evenness and of the diversity of a vocabulary or population be approximated through the expectation of these measures under the word or species frequency distribution. That leads to the assessment of the lack of diversity through measures of the variability of the mixing frequency distribution estimates described above.

Suggested Citation

  • Ginebra, Josep & Puig, Xavier, 2010. "On the measure and the estimation of evenness and diversity," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2187-2201, September.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:9:p:2187-2201
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    References listed on IDEAS

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    1. Solow Andrew & Polasky Stephen & Broadus James, 1993. "On the Measurement of Biological Diversity," Journal of Environmental Economics and Management, Elsevier, vol. 24(1), pages 60-68, January.
    2. Giron, Javier & Ginebra, Josep & Riba, Alex, 2005. "Bayesian Analysis of a Multinomial Sequence and Homogeneity of Literary Style," The American Statistician, American Statistical Association, vol. 59, pages 19-30, February.
    3. D. I. Holmes, 1992. "A Stylometric Analysis of Mormon Scripture and Related Texts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 155(1), pages 91-120, January.
    4. Alex Riba & Josep Ginebra, 2006. "Diversity of vocabulary and homogeneity of literary style," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 729-741.
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    1. Saralees Nadarajah & Vicente Cancho & Edwin Ortega, 2013. "The geometric exponential Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 355-380, August.
    2. Jordi Valero & Josep Ginebra & Marta Pérez-Casany, 2012. "Extended Truncated Tweedie-Poisson Model," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 811-829, September.
    3. Martínez-Rodríguez, A.M. & Sáez-Castillo, A.J. & Conde-Sánchez, A., 2011. "Modelling using an extended Yule distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 863-873, January.
    4. Shovan Chowdhury, 2014. "Compounded Generalized Weibull Distributions - A Unified Approach," Working papers 148, Indian Institute of Management Kozhikode.
    5. Xavier Puig & Josep Ginebra & Marti Font, 2010. "The Sichel model and the mixing and truncation order," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1585-1603.
    6. Aisling J. Daly & Jan M. Baetens & Bernard De Baets, 2018. "Ecological Diversity: Measuring the Unmeasurable," Mathematics, MDPI, vol. 6(7), pages 1-28, July.

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