![]() Differential entropy (described here) is commonly encountered in the literature, but it is a limiting case of the LDDP, and one that loses its fundamental association with discrete entropy. : 181–218 The actual continuous version of discrete entropy is the limiting density of discrete points (LDDP). Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. arXiv preprint arXiv: entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy, a measure of average (surprisal) of a random variable, to continuous probability distributions. A numeric vector if group.index is given. The other m components are the terms in the sum on the right-hand-side of (23).Ī non-negative number or +Inf if group.index is not given. The second component is the first term on the right-hand-side of (23). The first component is the left-hand-side of (23). In this case the output has 1 + 1 + m components, where m is the number of groups defined by group.index. If group.index is provided the relative entropy will be decompoesd using the chain rule stated in Lemma 3.1(i) of Pal and Wong (2013), see equation (23) there. Mathematically, this happens when p is not absolutely continuous with respect to q. If there is an index i where q = 0 but p > 0, then the relative entropy is Inf. It is not a metric as it is not symmetric and it does not satisfy the triangle inequality. It is also known as the Kullback-Leibler divergence and is usually denoted by H(p|q). Relative entropy can be thought of as a measure of distance between two probability distributions. If provided, the relative entropy will be decomposed according to the chain rule (see below for more details). RelativeEntropy ( p, q, group.index = NULL )Ī numeric vector representing a probability distribution.Ī numeric vector representing a probability distribution. VolStabModel: Volatility-Stabilized Model.SimMarketModel: Simulating a Market Model.RelValAnalysis: The RelValAnalysis Package.print.toymkt: Printing Toy Market Object.print.marketmodel: Printing Market Model Object.print.fgp: Printing Functionally Generated Portfolio Objects.print.capdist: Printing Capital Distribution Objects. ![]()
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