ddjeffreyspar: Distance between discrete probability distributions given the...

In dad: Three-Way / Multigroup Data Analysis Through Densities

Distance between discrete probability distributions given the probabilities on their common support

Description

Jeffreys divergence (symmetrized Kullback-Leibler divergence) between two discrete probability distributions on the same support (which can be a Cartesian product of q sets) , given the probabilities of the states (which are q-tuples) of the support.

Usage

ddjeffreyspar(p1, p2)

Arguments

p1	array (or table) the dimension of which is q. The first probability distribution on the support.
p2	array (or table) the dimension of which is q. The second probability distribution on the support.

Details

Jeffreys divergence ||p_1 - p_2|| between two discrete distributions p_1 and p_2 is given by the formula:

||p_1 - p_2|| = \sum_x{(p_1(x) - p_2(x)) log(p_1(x)/p_2(x))}

Author(s)

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Sabine Demotes-Mainard

References

Deza, M.M. and Deza E. (2013). Encyclopedia of distances. Springer.

See Also

ddjeffreys: Jeffreys distance between two estimated discrete distributions, given samples.

Other distances: ddchisqsympar, ddhellingerpar, ddjensenpar, ddlppar.

Examples

# Example 1
p1 <- array(c(1/2, 1/2), dimnames = list(c("a", "b"))) 
p2 <- array(c(1/4, 3/4), dimnames = list(c("a", "b"))) 
ddjeffreyspar(p1, p2)

# Example 2
x1 <- data.frame(x = factor(c("A", "A", "A", "B", "B", "B")),
                 y = factor(c("a", "a", "a", "b", "b", "b")))                 
x2 <- data.frame(x = factor(c("A", "A", "A", "B", "B")),
                 y = factor(c("a", "a", "b", "a", "b")))
p1 <- table(x1)/nrow(x1)                 
p2 <- table(x2)/nrow(x2)
ddjeffreyspar(p1, p2)

dad documentation built on Aug. 30, 2023, 5:06 p.m.