In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for findi...This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.展开更多
Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes ...Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes in the probability of attack, simultaneous effects on probability and loss, diversion of attack, and shared non-information defenses. Legal cases are then investigated to assess approximate magnitudes of external effects and the extent they are internalized by the legal system.展开更多
文摘In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
基金Supported by the National Natural Science Foundation of China(No.11071008)Scientific Foundations of Beijing Jiaotong University(No.2012JBM105)
文摘This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial （binomial） distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates （MLEs） of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.
文摘Extensions of the Gordon-Loeb [1] and the Gordon-Loeb-Lucyshyn-Zhou [2] models are presented based on mathematical equivalency with a generalized homeland security model. The extensions include limitations on changes in the probability of attack, simultaneous effects on probability and loss, diversion of attack, and shared non-information defenses. Legal cases are then investigated to assess approximate magnitudes of external effects and the extent they are internalized by the legal system.
