On the asymptotic approximation of inverse moment for non negative random variables. Issue 16 (18th August 2017)

• Record Type: Journal Article
• Authors: Yang, Wenzhi; Hu, Shuhe; Wang, Xuejun
• Is Part Of: Communications in statistics. Volume 46:Issue 16(2017)
• Page Start: 7787
• Page End: 7797
• Publication Date: 2017-08-18
• Subjects: Asymptotic approximation -- Growth rate -- Inverse moment -- Non negative random variables.; 60E15 -- 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.781648
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this paper, we have studied the asymptotic approximation of inverse moment. Let { Zn } be non negative random variables, where the truncated random variables satisfy the Rosenthal-type inequality. Denote . The inverse moment can be asymptotically approximated by, and the growth rate is presented as . Meanwhile, we obtain a result for a function f ( x ) satisfying certain conditions. On the other hand, if, then the growth rate is presented as | E ( a + Xn ) − α /( a + EXn ) − α − 1| = O (1/ EXn ). Our results generalize and improve some corresponding ones. Finally, some examples of inverse moment are illustrated.