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We explore properties of the entropy, Kullback-Leibler information, and mutual information for order statistics. The probability integral transformation plays a pivotal role in developing our results. We provide bounds for the entropy of order statistics and some results that relate entropy ordering of order statistics to other well-known orderings of(More)
Information-theoretic methodologies are increasingly being used in various disciplines. Frequently an information measure is adapted for a problem, yet the perspective of information as the unifying notion is overlooked. We set forth this perspective through presenting information-theoretic methodologies for a set of problems in probability and statistics.(More)
Seizure outcome is frequently described in terms of patients ever attaining remission or being in terminal remission. Outcomes are more complicated and, over many years, repeated remission and relapses may occur. These are difficult to quantify with standard survival techniques used in analysis of remission and relapse. The Markov process, which allows one(More)
SUMMARY. In this paper we propose a semiparamteric Bayesian approach to estimate the mixing function in a mixture of two exponential distributions. Unlike, the traditional mixture of two distributions in this paper we assume that the mixing parameter changes with time. Such models arise naturally in many applications such as software reliability engineering(More)
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 baseline cumulative hazard function is raised to a power function. Our(More)
Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix $$V$$ V into the product of two nonnegative matrices, $$W$$ W and $$H$$ H , such that $$V \sim WH$$ V ∼ W H . It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a(More)