# ddchisqsympar: Distance between discrete probability distributions given the... In dad: Three-Way / Multigroup Data Analysis Through Densities

## 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

 `1` ```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.

## Details

The chi-squared distance between two discrete distributions p_1 and p_2 is given by:

∑_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|| = ∑_x{(p_1(x) - p_2(x))^2}/(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.

`ddchisqsym`: chi-squared distance between two estimated discrete distributions, given samples.
Other distances: `ddhellingerpar`, `ddjeffreyspar`, `ddjensenpar`, `ddlppar`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# 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) ```