Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions {Compositional}

Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions

Description

Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions.

Usage

kl.diri(a, b, type = "KL")

Arguments

a

A vector with the parameters of the first Dirichlet distribution.

b

A vector with the parameters of the second Dirichlet distribution.

type

A variable indicating whether the Kullback-Leibler divergence ("KL") or the Bhattacharyya distance ("bhatt") is to be computed.

Details

Note that the order is important in the Kullback-Leibler divergence, since this is asymmetric, but not in the Bhattacharyya distance, since it is a metric.

Value

The value of the Kullback-Leibler divergence or the Bhattacharyya distance.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Ng Kai Wang, Guo-Liang Tian and Man-Lai Tang (2011). Dirichlet and related distributions: Theory, methods and applications. John Wiley & Sons.

See Also

diri.est, diri.nr

Examples

library(MASS)
a <- runif(10, 0, 20)
b <- runif(10, 1, 10)
kl.diri(a, b)
kl.diri(b, a)
kl.diri(a, b, type = "bhatt")
kl.diri(b, a, type = "bhatt")