Inequalities for sums of independent geometrical random variables
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We give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the functionF(p 1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p 1,...,pn) for every realt, whereX i are independent geometric random variables with parametersp i. A generalization to negative binomial random variables is also presented.
AMS subject classification (1991)Primary 60E15 Secondary 62E99
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