The assumption of proportional hazards (PH) fundamental to the Cox PH model sometimes may not hold in practice. In this paper, we propose a generalization of the Cox PH model in terms of the cumulative hazard function taking a form similar to the Cox PH model, with the extension that the...

In this paper, a semi-parametric generalization of the Cox model that permits crossing hazard curves is described. A theoretical framework for estimation in this model is developed based on penalized likelihood methods. It is shown that the optimal solution to the baseline hazard, baseline...

This paper first illustrates that a mutual information index detects and ranks dependence of a wide variety of absolutely continuous families, but the popular association and variance reduction indices fail to serve as such “common metrics”. We then elaborate on some theoretical merits of...

Which component is most important for a system's survival? We answer this question by ranking the information relationship between a system and its components. The mutual information (M) measures dependence between the operational states of the system and a component for a mission time as well...

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the...

It is well known that, without the assumption of independence between two nonnegative random variables X and Y, the survival function of X is not identifiable on the basis of the joint distribution function of Z = min(X, Y) and &dgr; = I(Z = Y). In this paper, we provide a simple condition in the...

Let Y1, Y2,..., Yn be non-negative random variables and let Y1 [less-than-or-equals, slant] Y(2) [less-than-or-equals, slant] ... [less-than-or-equals, slant] Y(n) denote order statistics. In this manuscript, we study several properties of Di = (n - i + 1)(Y(i) - Y(i-1)), I = 1,2,..., n, where...