Schur properties of convolutions of gamma random variables
  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. 
Farbod Roosta-Khorasani and Gabor J. Szekely
math.PR math.ST stat.TH