dad (version 4.1.6)

ddhellinger: Distance between probability distributions of discrete variables given samples

Description

Hellinger (or Matusita) distance between two multivariate (\(q > 1\)) or univariate (\(q = 1\)) discrete probability distributions, estimated from samples.

Usage

ddhellinger(x1, x2)

Value

The distance between the two probability distributions.

Arguments

x1, x2

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

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 Matusita distance between the discrete probability distributions of the samples are computed using the ddhellingerpar function.

References

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

See Also

ddhellingerpar: Hellinger metric (Matusita distance) between two discrete distributions, given the on their common support probabilities.

Other distances: ddchisqsym, ddjeffreys, ddjensen, ddlp.

Examples

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