Abstract
For a multivariate random vector X = (X 1,...,X n ) with a log-concave density function, it is shown that the minimum min{X 1,...,X n } has an increasing failure rate, and the maximum max{X 1,...,X n } has a decreasing reversed hazard rate. As an immediate consequence, the result of Gupta and Gupta (in Metrika 53:39–49, 2001) on the multivariate normal distribution is obtained. One error in Gupta and Gupta method is also pointed out.
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Hu, T., Li, Y. Increasing failure rate and decreasing reversed hazard rate properties of the minimum and maximum of multivariate distributions with log-concave densities. Metrika 65, 325–330 (2007). https://doi.org/10.1007/s00184-006-0079-2
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DOI: https://doi.org/10.1007/s00184-006-0079-2
Keywords
- Log-concavity
- Increasing failure rate
- Decreasing reversed hazard rate
- Multivariate normal distribution
- Elliptically contoured distributions