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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.

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.

Suggested Citation

  • Bi, L. & Mukherjea, A., 2011. "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)," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 611-613, May.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:5:p:611-613
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Kim, Bara & Kim, Jeongsim, 2022. "Identification of parameters from the distribution of the maximum or minimum of Poisson random variables," Statistics & Probability Letters, Elsevier, vol. 180(C).

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