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DEMONSTRATIO MATHEMATICAVol. XLIINo 12009P. N a t h , D. K . SinghON A S U M F O R M F U N C T I O N A L E Q U A T I O N R E L A T E D TOE N T R O P I E S AND SOME MOMENTS OF ADISCRETE RANDOM VARIABLEAbstract. The general solutions of a sum form functional equation have been obtained. The importance of its solutions in relation to the entropies and some moments ofa discrete random variable has been discussed.1. IntroductionFor n = 1 , 2 , . . . ; let= j ( p i , . . . ,pn) : Pi > 0, i = 1 , . . . , n; J2 Pi =1jdenote the set of all n-component complete discrete probability distributionswith nonnegative elements. For any probability distribution ( p i , . . . ,pn) £r n , the entropiesn(1-1)Hn(pi,...,pn)5^Pilog2pji=1= -are known as the Shannon entropies [7] with Hn :T n —> R, n = 1 , 2 , . . . ; Mdenoting the set of all real numbers and 01og2 0 : = 0.Given any probability distribution (pi,...
Demonstratio Mathematica – de Gruyter
Published: Jan 1, 2009
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