Characterizations of Levy Distribution via Sub-Independence of the Random Variables and Truncated Moments

Authors

Gholamhossein G. Hamedani, Marquette UniversityFollow
M. Ahsanullah, Rider University-LawrencevilleFollow
Seyed Morteza Najibi, Persian Gulf UniversityFollow

Document Type

Article

Language

eng

Publication Date

7-2015

Publisher

Pakistan Journal of Statistics

Source Publication

Pakistan Journal of Statistics

Source ISSN

1012-9367

Abstract

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In case of independence, characterization (i) reduces to that of Ahsanullah and Nevzorov (2014).

Comments

Published version. Pakistan Journal of Statistics, Vol. 31, No. 4 (July 2015): 417-425. © 2012 Pakistan Journal of Statistics. Used with permission.

Recommended Citation

Hamedani, Gholamhossein G.; Ahsanullah, M.; and Najibi, Seyed Morteza, "Characterizations of Levy Distribution via Sub-Independence of the Random Variables and Truncated Moments" (2015). Mathematics, Statistics and Computer Science Faculty Research and Publications. 451.
https://epublications.marquette.edu/mscs_fac/451