Stochastic Comparisons of Order Statistics from Gamma Distributions

Recently, Korwar has shown that a convolution of gamma distributions with a common shape parameter greater than 1 is larger in likelihood ratio order when the scale parameters are more dispersed in the sense of majorization. In this paper, we show that the order statistic of gamma distribution is larger in stochastic order when the shape parameter is smaller than or equal to 1 and the scale parameters are more dispersed in the sense of majorization. However, when the shape parameter is larger than 1, we only obtain that the minima is larger and maxima is smaller in stochastic order.