Diversity for Texts Builds in Language L(M_T): Indexes Based in Theory of Information

José Luis Usó-Doménech¹, Josué-Antonio Nescolarde-Selva^1, , Miguel Lloret-Climent¹ and Lucía González-Franco²

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

²Biodiversity Research Institute CIBIO, University of Alicante, Alicante, Spain

Cite this paper:
José Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Miguel Lloret-Climent and Lucía González-Franco. Diversity for Texts Builds in Language L(M_T): Indexes Based in Theory of Information. American Journal of Systems and Software. 2014; 2(5):113-120. doi: 10.12691/ajss-2-5-1

Abstract

If one has a distribution of words (SLUNs or CLUNS) in a text written in language L(M_T), and is adjusted one of the mathematical expressions of distribution that exists in the mathematical literature, some parameter of the elected expression it can be considered as a measure of the diversity. But because the adjustment is not always perfect as usual measure; it is preferable to select an index that doesn't postulate a regularity of distribution expressible for a simple formula. The problem can be approachable statistically, without having special interest for the organization of the text. It can serve as index any monotonous function that has a minimum value when all their elements belong to the same class, that is to say, all the individuals belong to oneself symbol, and a maximum value when each element belongs to a different class, that is to say, each individual is of a different symbol. It should also gather certain conditions like they are: to be not very sensitive to the extension of the text and being invariant to certain number of operations of selection in the text. These operations can be theoretically random. The expressions that offer more advantages are those coming from the theory of the information of Shannon-Weaver. Based on them, the authors develop a theoretical study for indexes of diversity to be applied in texts built in modeling language L(M_T), although anything impedes that they can be applied to texts written in natural languages.

Keywords:
diversity entropy information indetermination language model

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