Some new results on convolutions of heterogeneous gamma random variables

Authors:
Peng Zhao
Affiliations:
-
Venue:
Journal of Multivariate Analysis
Year:
2011

Citing 6
Cited 0

Schur properties of convolutions of exponential and geometric random variables

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On stochastic orders for sums of independent random variables

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Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables

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Mean residual life order of convolutions of heterogeneous exponential random variables

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On the right spread order of convolutions of heterogeneous exponential random variables

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On hazard rate ordering of the sums of heterogeneous geometric random variables

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Abstract

Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.