An equation associated with the distance between probability distributions

PL. Kannappan; P.K. Sahoo; J.K. Chung

Published: 1994-09-30

Vol. 8 (1994)

An equation associated with the distance between probability distributions

PL. Kannappan , P.K. Sahoo , J.K. Chung

Abstract

In this paper, we solve the functional equation
f₁(pr,qs) + f₂(ps,qr) = g(p,q)h(r,s) (p,q,r,s∈]0,1])
where f₁,f₂,g,h are complex-valued functions defined on ]0,1]. This functional equation is a generalization of a functional equation which was instrumental in the characterization of symmetric divergence of degree α in [3]. This equation arises in the characterization of symmetric weighted divergence of degree α and symmetric inset divergence of degree α.

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Kannappan, P., Sahoo, P., & Chung, J. (1994). An equation associated with the distance between probability distributions. Annales Mathematicae Silesianae, 8, 39–58. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14216

References

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4. H. Jeffreys, An invariant form for the prior probability in estimation problems, Proc. Roy. Soc. London Ser. A 186 (1946), 453-461.
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6. PL. Kannappan, P.K. Sahoo, J.K. Chung, On a functional equation associated with the symmetric divergence measures, Utilitas Math. 44 (1993), 75-83.
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PL. Kannappan

Affiliation:

Department of Pure Mathematics, University of Waterloo, Canada Canada

P.K. Sahoo

Affiliation:

Department of Mathematics, University of Louisville, USA United States

J.K. Chung

Affiliation:

Department of Applied Mathematics, South China University of Technology, People's Republic of China China

Vol. 8 (1994)
Published: 1994-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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