ON THE GEOMETRIC COMPOUNDING MODEL WITH APPLICATIONS
Chin-Yuan Hu
Gwo Dong Lin
Abstract: Under the geometric compounding model, we first investigate the relationship
between the compound geometric distribution and the underlying distribution, including the
preservation of the infinite divisibility property. An interesting upper bound for the tail
probability of the compound geometric distribution is provided by using only the mean of the
underlying distribution. Secondly, we apply the obtained results to understand better the
-class of life distributions. In particular, we strengthen a surprising result of Bhattacharjee
and Sengupta [5] and show that there are life distributions with the following
properties:
- the support of consists of countably infinite points,
- the coefficient of variation of is equal to one, and
- is not in the HNBUE class (the harmonic new better than used in expectation
class).
Finally, we apply geometric compounds to characterize the semi-Mittag-Leffler
distribution and extend a known result about the exponential distribution.
1991 AMS Mathematics Subject Classification: Primary 60E05, 60G50, 62E10,
44A10.
Key words and phrases: Geometric compounding model, -class, HNBUE class,
Laplace-Stieltjes transform, coefficient of variation, semi-Mittag-Leffler distribution.