EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 56(70), pp. 111--118 (1994)

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On Schur-convexity of some distribution functions

Milan Merkle and Ljiljana Petrovi\'c

Elektrotehnicki fakultet, Beograd, Yugoslavia and Prirodno-matematicki fakultet, Kragujevac, Yugoslavia

Abstract: If $X_1,\dots,X_n$ are independent geometric random variables with parameters $p_1,\dots,p_n$ respectivelly, we prove that the function $F(p_1,\dots,p_n;t) = P(X_1+\dots+X_n\leqt)$ is Schur-concave in $(p_1,\dots,p_n)$ for every real $t$. We also give a new proof for a theorem due to P. Diaconis on Schur-convexity of distribution fuction of linear combination of two exponential random variables.

Classification (MSC2000): 60E15

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Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition