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    • On the discretization of probability density functions and the continuous Rényi entropy

      Diógenes Campos

      Volume 85 Issue 6 December 2015 pp 1073-1087

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/085/06/1073-1087

    • Keywords

       

      Probability density function; Rényi entropy; differential (continuous) entropy; discretization method; mean-value theorem for integrals.

    • Abstract

       

      On the basis of second mean-value theorem (SMVT) for integrals, a discretization method is proposed with the aim of representing the expectation value of a function with respect to a probability density function in terms of the discrete probability theory. This approach is applied to the continuous Rényi entropy, and it is established that a discrete probability distribution can be associated to it in a very natural way. The probability density functions for the linear superposition of two coherent states is used for developing a representative example.

    • Author Affiliations

       

      Diógenes Campos1

      1. Academia Colombiana de Ciencias Exactas, Físicas y Naturales, ACCEFYN, Bogotá, Colombia

    • Dates

       
      Published
      December 2015
      Manuscript received
      27 June 2014
      Manuscript revised
      11 September 2014
      Accepted
      27 September 2014
      Early published
      19 July 2015

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