Extremal limit laws for a class of bivariate Poisson vectors
It is well known that conventional extreme value limit laws break down for the Poisson distribution: no normalization can be found to avoid degeneracy of the limit law of sample maxima. Anderson et al. (Ann. Appl. Probab. 7 (1997) 953) tackled this problem with a triangular array argument, letting both the sample size and Poisson mean grow at appropriate rates. This leads to a Gumbel limit law for sample maxima. In applications, this means that it may be appropriate to model extremes of Poisson processes using standard extreme value models and techniques. This paper extends the limit results to a class of bivariate Poisson distributions. Suitably normalized, and with a degree of dependence that is also permitted to grow at a suitable rate, we find that the limit distribution corresponds to the class of bivariate extreme value models that would have arisen, had the population been bivariate normal, cf. Hüsler and Reiss (Statist. Probab. Lett. 7 (1989) 283). This adds weight to the argument that, for practical applications involving Poisson variables, even in the presence of dependence, standard extreme value models can be applied, despite the degeneracy that arises by applying the usual asymptotic argument.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 54 (2001)
Issue (Month): 4 (October)
|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|
References listed on IDEAS
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.:
- Hüsler, J., 1994. "Maxima of bivariate random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 385-394, December.
- Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:373-379. 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: (Shamier, Wendy)
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.