Next we investigate the convexity theory of programming under probabilistic constraints. Prekopa [63, 74] has proved that if T is an r x n random matrix with independent, normally distributed rows such that their covariance matrices are constant multiples of each other, then the function h(x) = P(Tx ac b) is quasi-concave in Rn , where b is a constant vector. We prove that, under same condition, the converse is also true, a special quasi-concavity of h(x) implies the above-mentioned property of the covariance matrices.Dawson and Sankoff [22] proposed a sharp lower bound for the probability of the union of events using the first two ... be formulated as discrete binomial moment problems and presented linear programming problems, with input data S1, ..., Sm, anbsp;...

Title | : | New Results in Probability Bounding, a Convexity Statement and Unimodality of Multivariate Discrete Distributions |

Author | : | Munevver Mine Subasi |

Publisher | : | ProQuest - 2008 |

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