Poisson distributions: Identification of parameters from the distribution of the maximum and a conjecture on the partial sums of the power series for exp(x)
Let (X1,X2,...,Xn) be n independent Poisson (real) random variables with (positive) parameters [lambda]1,[lambda]2,...,[lambda]n respectively. Then does the distribution of the maximum of the X(i)s determine uniquely the parameters [lambda]i? This is the question that we discuss in this note. This question brings up an interesting, probably difficult, conjecture involving the partial sums of the power series for exp(x). A similar conjecture comes up in the context of the corresponding minimum problem.
Volume (Year): 81 (2011)
Issue (Month): 5 (May)
|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.:
- Basu, A. P. & Ghosh, J. K., 1978. "Identifiability of the multinormal and other distributions under competing risks model," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 413-429, September.
- Mukherjea, A. & Nakassis, A. & Miyashita, J., 1986. "The problem of identification of parameters by the distribution of the maximum random variable," Journal of Multivariate Analysis, Elsevier, vol. 18(2), pages 178-186, April.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:611-613. 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 references are entirely missing, you can add them using this form.