Bounds for factorial moments of discrete distributions

Article type: Research Article

Authors: Mahmood, Munir^{a; *} | Edwards, Phillip^b

Affiliations: [a] Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, Hawally 32093, P.O. Box 7207, Kuwait | [b] Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3168, Australia

Correspondence: [*] Corresponding author. E-mail: munirmahmood2003@gmail.com.

Abstract: The arithmetic mean (AM) and geometric mean (GM) of a set of non-negative real numbers a1,a2,…,an are defined by AM=1n(a1+a2+…+an and GM=(a1,a2…an)1n with equality if and only if a1=a2=…=an. This paper uses the well known algebraic inequality GM⩽AM to derive bounds for factorial moments of a number of discrete probability distributions. As a consequence, a relationship is derived between various factorial moments and the factorial polynomial. We consider upper bounds for factorial moments. It is interesting to see that some of these bounds reduce to bounds for the factorial polynomial and bounds for n!.

Keywords: Discrete probability distribution, factorial moment, factorial polynomial

DOI: 10.3233/MAS-2007-2302

Journal: Model Assisted Statistics and Applications, vol. 2, no. 3, pp. 121-124, 2007