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

Volume 11, Number 5, September 2015 - SC 50 - pp. 509-512

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 June 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.

 

References: 10

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