Abstract
In this paper, we study ordering properties of convolutions of heterogeneous Erlang and Pascal random variables in terms of the majorization order [ p -larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [hazard rate order, mean residual life order]. We establish, among other things, that weak majorization order [ p -larger order, reciprocal majorization order] between scale parameter vectors and majorization order between shape parameter vectors imply likelihood ratio order [hazard rate order, mean residual life order] between convolutions of two heterogeneous Erlang or Pascal sets of variables. These results strengthen and generalize some of the results known from the literature.
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