On a new multivariate IFR ageing notion based on the standard construction
A. Arriaza
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain
Search for more papers by this authorF. Belzunce
Departamento Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
Search for more papers by this authorJ. Mulero
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Alicante, Apartado de correos 99, Alicante, 03080 Spain
Search for more papers by this authorCorresponding Author
A. Suárez-Llorens
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain
Correspondence to: A. Suárez-Llorens, Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain.
E-mail: [email protected]
Search for more papers by this authorA. Arriaza
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain
Search for more papers by this authorF. Belzunce
Departamento Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
Search for more papers by this authorJ. Mulero
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Alicante, Apartado de correos 99, Alicante, 03080 Spain
Search for more papers by this authorCorresponding Author
A. Suárez-Llorens
Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain
Correspondence to: A. Suárez-Llorens, Departamento Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain.
E-mail: [email protected]
Search for more papers by this authorAbstract
Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the classical univariate convex transform order. A new multivariate generalization of the convex transform order has recently been proposed in the literature. In this work, we propose a new multivariate IFR notion for multivariate distributions based on comparisons in this new order with a properly defined exponentially distributed random vector. Properties, applications, and illustrations of this new notion are given as well. Copyright © 2016 John Wiley & Sons, Ltd.
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