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This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.

Interconnections between occurrence times of nonhomogeneous Poisson processes, record values, minimal repair times, and the relevation transform are explained. A number of properties of the distributions of occurrence times and interoccurrence times of a nonhomogeneous Poisson process are proved when the mean-value function of the process is convex, starshaped, or superadditive. The same results hold for upper record values of independently identically distributed random variables from IFR, IFRA, and NBU distributions.

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Hazard function, cumulative hazard function, mean residual lifetime function, NBU, IFR, Kullback-Leibler discrimination information, MDI principle,