PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 56(70), pp. 111--118 (1994)
On Schur-convexity of some distribution functions
Milan Merkle and Ljiljana Petrovi\'cElektrotehnicki 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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