Title: Concavity of maximum entropy through modified Burg's entropy subject to its prescribed mean

Authors: Amritansu Ray; Sanat Kumar Majumder

Addresses: Department of Mathematics, Rajyadharpur Deshbandhu Vidyapith, Serampore, Hooghly – 712203, West Bengal, India ' Department of Mathematics, IIEST [formerly Bengal Engineering and Science University (BESU), Shibpur], Howrah – 711103, West Bengal, India

Abstract: The paper deals with the concavity of maximum entropy when maximised subject to its mean being prescribed. This is an extension of Burg's entropy maximisation with the said constraint. It is proved that when modified Burg' entropy is maximised subject to its mean m being prescribed then maximum entropy S_max will be concave function of m and it is shown unlike Burg's entropy, its maximum value increases with number n. Example is given to illustrate the work at the end. Various examples are given to illustrate the total work and a particular example with tables and graph is given at the end.

Keywords: modified Burg's entropy; Shannon's entropy; maximum entropy principle; maximum entropy probability distribution; concavity; prescribed mean.

DOI: 10.1504/IJMOR.2016.076779

International Journal of Mathematics in Operational Research, 2016 Vol.8 No.4, pp.393 - 405

Received: 07 Apr 2014
Accepted: 27 Aug 2014
Published online: 01 Jun 2016 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article