Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables

Peng Zhao and N. Balakrishnan

Statistics & Probability Letters, 2010, vol. 80, issue 11-12, 969-974

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.

Keywords: Majorization; p-larger; order; Reciprocal; majorization; order; Likelihood; ratio; order; Hazard; rate; order; Mean; residual; life; order; Erlang; convolution; Pascal; convolution (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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