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On the Multivariate Normal Hazard

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  • Gupta, Pushpa L.
  • Gupta, Ramesh C.

Abstract

It is well known that the hazard rate of a univariate normal distribution is increasing. In this paper, we prove that the hazard gradient, in the case of general multivariate normal distribution, is increasing in the sense of Johnson and Kotz.

Suggested Citation

  • Gupta, Pushpa L. & Gupta, Ramesh C., 1997. "On the Multivariate Normal Hazard," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 64-73, July.
    • Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:64-73
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    References listed on IDEAS

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    1. Marshall, Albert W., 1975. "Some comments on the hazard gradient," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 293-300, July.
    2. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
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    Cited by:

    1. Ma, Chunsheng, 2000. "A Note on the Multivariate Normal Hazard," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 282-283, May.
    2. Ramesh Gupta & N. Balakrishnan, 2012. "Log-concavity and monotonicity of hazard and reversed hazard functions of univariate and multivariate skew-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 181-191, February.
    3. Jorge Navarro & Jose Ruiz, 2004. "A characterization of the multivariate normal distribution by using the hazard gradient," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 361-367, June.

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