On Stochastic Orders for Sums of Independent Random Variables
In this talk, it will be shown that a convolution of uniform distributions (a) is more dispersed
and (b) has a smaller hazard rate when the scale parameters of the uniform distributions are more
dispersed in the sense of majorization. It will also be shown that a convolution of gamma distributions
with a common shape parameter greater than 1 is larger in (a) the likelihood ratio order and (b)the
dispersive order when the scale parameters of the gamma distributions are more dispersed in the sense
of majorization.