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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)

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  • Bi, L.
  • Mukherjea, A.
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 81 (2011)
    Issue (Month): 5 (May)
    Pages: 611-613

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    Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:611-613

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    Keywords: Poisson distributions Identification of the parameters The distribution of the maximum;

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