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The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case

Author

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  • Mukherjea, Arunava
  • Stephens, Richard

Abstract

Let (Xi, Yi, Zi), i = 1, 2, ..., m, be a number of independent random vectors each with a non-singular trivariate normal distribution function with non-zero correlations and zero means. Let (X, Y, Z) be their maximum, i.e., X = maxiXi, Y = maxiYi, and Z = maxiZi. In this paper, we show that the distribution of (X, Y, Z) uniquely determines the parameters of the distributions of (Xi, Yi, Zi), 1

Suggested Citation

  • Mukherjea, Arunava & Stephens, Richard, 1990. "The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 95-115, July.
    • Handle: RePEc:eee:jmvana:v:34:y:1990:i:1:p:95-115
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    Citations

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    Cited by:

    1. Enkelejd Hashorva, 2005. "Asymptotics and Bounds for Multivariate Gaussian Tails," Journal of Theoretical Probability, Springer, vol. 18(1), pages 79-97, January.
    2. Ming Dai & Arunava Mukherjea, 2001. "Identification of the Parameters of a Multivariate Normal Vector by the Distribution of the Maximum," Journal of Theoretical Probability, Springer, vol. 14(1), pages 267-298, January.
    3. 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).
    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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