dad (version 4.1.6)

ddchisqsym: Distance between probability distributions of discrete variables given samples

Description

Symmetrized chi-squared distance between two multivariate (\(q > 1\)) or univariate (\(q = 1\)) discrete probability distributions, estimated from samples.

Usage

ddchisqsym(x1, x2)

Value

The distance between the two probability distributions.

Arguments

x1, x2

vectors or data frames of \(q\) columns (can also be a tibble).

If they are data frames and have not the same column names, there is a warning.

Author

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

Details

Let \(p_1\) and \(p_2\) denote the estimated probability distributions of the discrete samples \(x_1\) and \(x_2\). The symmetrized chi-squared distance between the discrete probability distributions of the samples are computed using the ddchisqsympar function.

References

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

See Also

ddchisqsympar: chi-squared distance between two discrete distributions, given the probabilities on their common support.

Other distances: ddhellinger, ddjeffreys, ddjensen, ddlp.

Examples

# Example 1
x1 <- c("A", "A", "B", "B")
x2 <- c("A", "A", "A", "B", "B")
ddchisqsym(x1, x2)

# 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")))
ddchisqsym(x1, x2)