摘要：Let \{Yn\} be a sequence of nonnegative random variables (rvs), and Sn=∑j=1nYj , n≥1 . It is first shown that independence of Sk-1 and Yk , for all 2≤ k≤n , does not imply the independence of Y1,Y2,...,Yn . When Yj 's are identically distributed exponential \Exp(α) variables, we show that the independence of Sk-1 and Yk , 2W≤k≤n , implies that the Sk follows a gamma G(α,k) distribution for every 1≤k≤n . It is shown by a counterexample that the converse is not true. We show that if X is a non-negative integer valued rv, then there exists, under certain conditions, a rv Y≥ 0 such that N(Y)\stackrel{\cal{L}}{=}X , where {N(t)} is a standard (homogeneous) Poisson process, and obtain the Laplace-Stieltjes transform of Y . This leads to a new characterization for the gamma distribution. It is also shown that a G(α,k) distribution may arise as the distribution of Sk , where the components are not necessarily exponential. Several typical examples are discussed.
