On multivariate mean remaining life functions

The concept of the mean remaining life function is extended to the multivariate case. Some general characterization properties of multivariate mean remaning life functions (mmrl) are studied, it is shown that they determine the joint pdf uniquely. Inter alia a basic convergence result is proved for a sequence of mmrl functions. The multivariate loss of memory property of a pdf is characterized in terms of the mmrl function. The relationship between the mmrl function and the hazard-gradient is discussed.