IJPAM: Volume 39, No. 2 (2007)

ON NECESSARY AND SUFFICIENT CONDITIONS FOR
CONVERGENCE TO THE GEOMETRIC DISTRIBUTION

Dodi Devianto$^1$, Katsuo Takano$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Ibaraki University
2-1-1Bunkyo, Mito, Ibaraki, 310-8512, JAPAN
$^1$e-mail: ddevianto@fmipa.unand.ac.id
$^2$e-mail: ktaka@mx.ibaraki.ac.jp


Abstract.By using Lévy representation of characteristic function we show necessary and sufficient conditions for convergence of a sequence of distribution functions of sums of infinitesimal system of random variables to the geometric distribution.

Received: June 11, 2007

AMS Subject Classification: 60D05, 60E07

Key Words and Phrases: geometric distribution, negative-binomial distribution, Lévy representation, infinitesimal system of random variables

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 2