dad (version 4.1.6)

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

Description

Symmetrized chi-squared distance 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

ddchisqsympar(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.

Author

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

Details

The chi-squared distance between two discrete distributions \(p_1\) and \(p_2\) is given by: $$\sum_x{(p_1(x) - p_2(x))^2}/p_2(x)$$

Then the symmetrized chi-squared distance is given by the formula: $$||p_1 - p_2|| = \sum_x{(p_1(x) - p_2(x))^2}/(p_1(x) + p_2(x))$$

References

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

See Also

ddchisqsym: chi-squared distance between two estimated discrete distributions, given samples.

Other distances: ddhellingerpar, ddjeffreyspar, 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"))) 
ddchisqsympar(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)
ddchisqsympar(p1, p2)