Topsoe: Topsoe Distance
In patrickreidy/distdist: Distances on Distributions

Description Usage Arguments Details Value See Also

Compute the Topsoe distance between two probability distributions.

1 2	## S4 method for signature 'Distribution,Distribution' Topsoe(p1, p2, metric = FALSE)

`p1, p2`	`Distributions`.
`metric`	A logical. If `TRUE`, then the square root of the Topsoe distance is returned, which satisfies the properties of a metric.

Let p1 and p2 denote the vectors of probability mass assigned by two distributions defined on the same state space; furthermore, let these distributions be strictly positively-valued. Let p3 = (p1 + p2) / 2. Then, the Topsoe distance between p1 and p2 is given by KullbackLeibler(p1, p3) + KullbackLeibler(p2, p3).

The Topsoe distance is a symmetric function based on Kullback-Leibler divergence. It is the sum of the Kullback-Leibler divergence of the distribution interpolated between p1 and p2, from either distribution. Equivalently, the Topsoe distance is twice the Jensen-Shannon divergence with a = 1/2.

The Topsoe distance is not a metric (i.e., it does not satisfy the triangle inequality); however, its square root is a metric.

The Topsoe distance or the Topsoe metric (if metric = TRUE) between p1 and p2.

Kullback-Leibler, Jensen-Shannon

patrickreidy/distdist documentation built on May 22, 2019, 12:40 p.m.