ON THE INFINITE DECOMPOSABILITY OF THE GEOMETRIC DISTRIBUTION
Vol. 9(1) Jan. 2021, No. 21, pp. 243-247
CHRISTOPHE CHESNEAU AND JOSE LUIS PALACIOS
In this note, we prove a new result on the infinite decomposability of the geometric distribution. More precisely, we show that a random variable following the geometric distribution can be written as any sum of random variables following a modified geometric distribution at 0 plus one random variable following the geometric distribution, all of them independent. Similar results are obtained for other distributions defined by a sum of random variables involving the geometric distribution.