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In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
The dual divergence to a Bregman divergence is the divergence generated by the convex conjugate F * of the Bregman generator of the original divergence. For example, for the squared Euclidean distance, the generator is x 2 {\displaystyle x^{2}} , while for the relative entropy the generator is the negative entropy x log x ...
In probability theory, an -divergence is a certain type of function (‖) that measures the difference between two probability distributions and . Many common divergences, such as KL-divergence , Hellinger distance , and total variation distance , are special cases of f {\displaystyle f} -divergence.
Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in Kullback (1959, pp. 6–7, §1.3 Divergence). The asymmetric "directed divergence" has come to be known as the Kullback–Leibler divergence, while the symmetrized "divergence" is now referred to as the Jeffreys divergence.
As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field of non-zero order k is written as =, a contraction of a tensor field of order k − 1. Specifically, the divergence of a vector is a scalar.
A "positive divergence" or "bullish divergence" occurs when the price makes a new low but the MACD does not confirm with a new low of its own. A "negative divergence" or "bearish divergence" occurs when the price makes a new high but the MACD does not confirm with a new high of its own. [8]
In a solenoidal vector field (i.e., a vector field where the divergence is zero everywhere), the field lines neither begin nor end; they either form closed loops, or go off to infinity in both directions. If a vector field has positive divergence in some area, there will be field lines starting from points in that area.
Conditioning on a third random variable may either increase or decrease the mutual information: that is, the difference (;) (; |), called the interaction information, may be positive, negative, or zero. This is the case even when random variables are pairwise independent.