Diversity for Texts Builds in Language L(M_T) II: Indexes Based in Abundances

José Luis Usó-Doménech¹, Josué-Antonio Nescolarde-Selva^{1, 2,} , Miguel Lloret-Climent¹ and Meng Fan²

¹Department of Applied Mathematics, University of Alicante, Alicante, Spain

²School of Mathematics and Statistics, Northeast Normal University, Changchun, China

Cite this paper:
José Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Miguel Lloret-Climent and Meng Fan. Diversity for Texts Builds in Language L(M_T) II: Indexes Based in Abundances. American Journal of Systems and Software. 2016; 4(2):32-39. doi: 10.12691/ajss-4-2-1

Abstract

One saw previously that indications of diversity I_T and the one of Shannon permits to characterize globally by only one number one fundamental aspects of the text structure. However a more precise knowledge of this structure requires specific abundance distributions and the use, to represent this one, of a suitable mathematical model. Among the numerous models that would be either susceptible to be proposed, the only one that present a real convenient interest are simplest. One will limit itself to study applied three of it to the language L(M_T): the log-linear, the log-normal and Mac Arthur's models very used for the calculation of the diversity of the species of ecosystems, and used, we believe that for the first time, in the calculation of the diversity of a text written in a certain language, in our case L(M_T). One will show advantages and inconveniences of each of these model types, methods permitting to adjust them to text data and in short tests that permit to decide if this adjustment is acceptable.

Keywords:
abundances complex systems distribution language law of Zipf model probability text

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