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ON A SUM FORM FUNCTIONAL EQUATION RELATED TO ENTROPIES AND SOME MOMENTS OF A DISCRETE RANDOM VARIABLE

ON A SUM FORM FUNCTIONAL EQUATION RELATED TO ENTROPIES AND SOME MOMENTS OF A DISCRETE RANDOM... 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,... http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON A SUM FORM FUNCTIONAL EQUATION RELATED TO ENTROPIES AND SOME MOMENTS OF A DISCRETE RANDOM VARIABLE

Demonstratio Mathematica , Volume 42 (1): 14 – Jan 1, 2009

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References (7)

Publisher
de Gruyter
Copyright
© by P. Nath
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2009-0109
Publisher site
See Article on Publisher Site

Abstract

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,...

Journal

Demonstratio Mathematicade Gruyter

Published: Jan 1, 2009

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