This article is cited in 1 paper

A new characterization of the Poisson distribution

V. M. Kruglov

M. V. Lomonosov Moscow State University

Abstract: In this note we show that an infinitely divisible (i.d.) distribution function $F$ is Poisson if and only if it satisfies the conditions $F(+0)>0$, for any $0<\varepsilon<1$
$$ \int_{-\infty}^{1-\varepsilon}\frac{|x|}{1+|x|}\,dF=0, $$
and for any $0<\alpha<1$
$$ \int_0^\infty e^{\alpha x\ln(x+1)}\,dF<\infty $$


UDC: 519

Received: 23.04.1975

 English version: Mathematical Notes, 1976, 20:6, 1049–1051

Bibliographic databases:

• 
•