Stochastic Comparisons Of Order Statistics And Linear Combinations Of Random Variables

This thesis consists of two parts. In the first part, we study stochastic comparisons of order statistics from a homogeneous sample and from a heterogeneous sample in the sense of the usual stochastic order. This part generalized the main result of Ma (1997) from independent samples to dependent samples. In the second part, we present a simple proof for a result concerning the dispersive ordering between linear combinations of uniform random variables. The result states that a linear combination of uniform random variables is more dispersed when the scale parameters of the uniform random variables are more dispersed in the sense of majorization. Its first proof was given by Korwar (2002) and Khaledi and Kochar (2002).