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A Simple Analytic Approximation for Entropy of Student-t Distribution and its Relation with Normal Distribution

SC IJPE 50

LAMBERT  PIERRAT1 and SAMUEL  KOTZ2

1  LJ - Consulting &  LJK-LAB, UMR CNRS 5224, Grenoble Alps University, 21 Allée Jean Wiener, 38040 Saint Martin d’Hères Cedex, FRANCE
2  George Washington University, Washington DC, USA (Deceased)

Received on:  Julne 24, 2014
Revised on:  December 15, 2014

 

Abstract:

In the expression corresponding to the Shannon’s entropy of the Student-t distribution the gamma and digamma integral functions appear. We propose a simple analytical approximation for its entropy function for all degrees of freedom which assures the continuity between normal and Cauchy distributions. A possible application is to define a normal distribution “equivalent” of the Student-t, usable for any degrees of freedom (integral or fractional) larger than 7.

 

Status: Published on Vol.11 No. 5 Septemver 2015 issue of IJPE

 
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