A Note on the Inverse Moment for the Non Negative Random Variables

作者：Hu Shuhe; Wang Xinghui; Yang Wenzhi^*; Wang Xuejun

来源：Communications in Statistics - Theory and Methods, 2014, 43(8): 1750-1757.

DOI：10.1080/03610926.2012.673677

• Binomial distribution
• Inverse moment
• Rosenthal-type inequality

Let {Z(n)} be a sequence of non negative random variables satisfying a Rosenthal-type inequality and , where {M-n} is a sequence of positive real numbers. By using the Rosenthal-type inequality, the inverse moment E(a + X-n)(- alpha) can be asymptotically approximated by (a + EXn)(- alpha) for all a > 0 and alpha > 0. Furthermore, we show that E[f(X-n)](- 1) can be asymptotically approximated by [f(EXn)](- 1) for a function f( center dot ) satisfying certain conditions. Our results generalize and improve some corresponding results, which can allow immediate applications to compute the inverse moments for the non negative random variables whose distributions are such as Binomial distribution, Poisson distribution, Gamma distribution, etc.

• 出版日期2014-4-18
• 单位安徽大学