Schur properties of convolutions of gamma random variables
Farbod Roosta-Khorasani, Gabor J. Szekely
TL;DR
This paper establishes conditions under which convolutions of heterogeneous gamma random variables can be compared using stochastic order, based on Schur convexity properties, with practical applications demonstrated.
Contribution
It introduces new sufficient conditions for stochastic ordering of gamma convolutions using Schur convexity, expanding understanding of their probabilistic behavior.
Findings
Conditions for stochastic comparison of gamma convolutions are derived.
Schur convexity of the CDF characterizes convolution comparisons.
Practical examples illustrate the applicability of the results.
Abstract
Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative distribution function of the convolutions. Some examples of the practical applications of our results are given.
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