Enlargement of the Class of Geometrically Infinitely Divisible Random Variables
Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 126
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
The class of negative binomial infinitely divisible random
variables is introduced in the following way: Random variable $Y$ is
called {\it negative binomial infinitely divisible\/} if there exist
i.i.d. random variables $X^{(1)}_p,X^{(2)}_p,\dots$, $p\in(0,1)$,
independent of $Y$ and $\nu^{(r)}_p$ and such that
$
Y \mathrel{\mathop=^{\text {\rm d}}} łim_{p\to 0} \sum^{\nu_p^{(r)}}_{j=1}
X^{(j)}_p,
$
where $\nu^{(r)}_p$ has negative binomial law.
\par
The representation of characteristic functions from the class of
negative binomial infinitely divisible random variables is given and
also some related properties discussed. When $r=1$ the above class
reduces to the well known class of geometrically infinitely divisible
random variables.
Classification :
60E07
@article{PIM_1993_N_S_54_68_a15,
author = {Slobodanka Jankovi\'c},
title = {Enlargement of the {Class} of {Geometrically} {Infinitely} {Divisible} {Random} {Variables}},
journal = {Publications de l'Institut Math\'ematique},
pages = {126 },
year = {1993},
volume = {_N_S_54},
number = {68},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a15/}
}
TY - JOUR AU - Slobodanka Janković TI - Enlargement of the Class of Geometrically Infinitely Divisible Random Variables JO - Publications de l'Institut Mathématique PY - 1993 SP - 126 VL - _N_S_54 IS - 68 UR - http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a15/ LA - en ID - PIM_1993_N_S_54_68_a15 ER -
Slobodanka Janković. Enlargement of the Class of Geometrically Infinitely Divisible Random Variables. Publications de l'Institut Mathématique, _N_S_54 (1993) no. 68, p. 126 . http://geodesic.mathdoc.fr/item/PIM_1993_N_S_54_68_a15/