In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 16, No. 01 ( 1979-03), p. 138-153
Abstract:
Any probability distribution on [0,∞) can function as the mixing distribution for a Poisson mixture , i.e. a mixture of Poisson distributions. The mixing distribution is called quasi-infinitely divisible ( q.i.d. ) if it renders the Poisson mixture infinitely divisible, or λ -q.i.d. if it does so after scaling by a factor λ & gt; 0, or ∗-q.i.d. if it is λ-q.i.d. for some λ. These classes of distributions include the infinitely divisible distributions, and each exhibits many of the properties of the latter class but in weakened form. The paper presents the main properties of the classes and the class of Poisson mixtures, including characterisations of membership, relation with cumulants, and closure properties. Examples are given that establish among other things strict inclusions between the classes of mixing distributions.
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
DOI:
10.1017/S0021900200046271
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1979
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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