Multivariate extensions of univariate life distributions (Q1272745)

For \(i=1,2,\dots,p\), let \(F_i\) be a univariate distribution function. Denote \(\overline F_i=1-F_i\) and \(R_i=-\log\overline F_i\). The authors study the multivariate survival function \(\overline F\) defined by \[ \overline F(x_1,x_2,\dots,x_p)=\exp\left[-\left\{\sum^p_{i=1}\bigl(R_i(x_i)\bigr)^\nu\right\}^{1/\nu}\right], \] where \(\nu\geq 1\) is the dependency parameter. In particular, they obtain an expression for the corresponding density function, and they show some preservations of aging properties. The nature of dependence of \(\overline F\) is also examined. Finally the authors study the particular case where each \(F_i\) is a univariate Weibull distribution.