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Failure rate of the minimum and maximum of a multivariate normal distribution

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Abstract.

It is well known that if the parent distribution has a nonnegative support and has increasing failure rate (IFR), then all the order statistics have IFR. The result is not necessarily true in the case of bivariate distributions with dependent structures. In this paper we consider a multivariate normal distribution and prove that, the distributions of the minimum and maximum retain the IFR property.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469-5752, USA (e-mail: RCGUPTA@maine.maine.edu), , , , , , US

    Pushpa L. Gupta & Ramesh C. Gupta

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  1. Pushpa L. Gupta
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  2. Ramesh C. Gupta
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Received: September 1999

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Gupta, P., Gupta, R. Failure rate of the minimum and maximum of a multivariate normal distribution. Metrika 53, 39–49 (2001). https://doi.org/10.1007/s001840000093

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  • DOI: https://doi.org/10.1007/s001840000093

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