On the sample ranges from heterogeneous exponential variables

In this paper, the sample range from a heterogeneous exponential sample is shown to be larger than that from a homogeneous exponential sample in the sense of the star ordering. Then, by using this result, some equivalent characterizations of stochastic comparisons of sample ranges with respect to various stochastic orders are established. In this process, two open problems mentioned in Mao and Hu (2010) [16] are solved. The main results established here extend and strengthen several known results in the literature including those of Khaledi and Kochar (2000) [8], Zhao and Li (2009) [22] and Genest et al. (2009) [7].