Exponential families of mixed Poisson distributions
If I=(I1,...,Id) is a random variable on [0,[infinity])d with distribution [mu](d[lambda]1,...,d[lambda]d), the mixed Poisson distribution MP([mu]) on is the distribution of (N1(I1),...,Nd(Id)) where N1,...,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,[infinity])d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+...+vqYq for some q[less-than-or-equals, slant]d, for some vectors v0,...,vq of [0,[infinity])d with disjoint supports and for independent standard real gamma random variables Y1,...,Yq.
Volume (Year): 98 (2007)
Issue (Month): 6 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bobecka, Konstancja & Wesolowski, Jacek, 2004. "Multivariate Lukacs theorem," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 143-160, November.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1283-1292. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.