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The problem of identification of parameters by the distribution of the maximum random variable

Author

Listed:
  • Mukherjea, A.
  • Nakassis, A.
  • Miyashita, J.

Abstract

Suppose that X1, X2,..., Xn are independently distributed according to certain distributions. Does the distribution of the maximum of {X1, X2,..., Xn} uniquely determine their distributions? In the univariate case, a general theorem covering the case of Cauchy random variables is given here. Also given is an affirmative answer to the above question for general bivariate normal random variables with non-zero correlations. Bivariate normal random variables with nonnegative correlations were considered earlier in this context by T. W. Anderson and S. G. Ghurye.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:18:y:1986:i:2:p:178-186
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. Bi, L. & Mukherjea, A., 2010. "Identification of parameters and the distribution of the minimum of the tri-variate normal," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1819-1826, December.
    4. Irene Hueter, 2000. "Recovering a Family of Two-Dimensional Gaussian Variables from the Minimum Process," Journal of Theoretical Probability, Springer, vol. 13(4), pages 939-950, October.

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