In this paper, we study the convolutions of heterogeneous exponential and geometric random variables in terms of the weakly majorization order (>=(w)) of parameter vectors and the likelihood ratio order (>=(Ir)). It is proved that >=(w) order between two parameter vectors implies >=(Ir) order between convolutions of two heterogeneous exponential (geometric) samples. For the two-dimensional case, it is found that there exist stronger equivalent characterizations. These results strengthen the corresponding ones of Boland et al. [Boland, P.J., El-Neweihi, E., Proschan, F., 1994. Schur properties of convolutions of exponential and geometric random variables. journal of Multivariate Analysis 48, 157-167] by relaxing the conditions on parameter vectors from the majorization order (>=(m)) to >=(w) order.
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