Concavity of maximum entropy through modified Burg's entropy subject to its prescribed mean (Q2204216)

Summary: 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.