ddhellinger function

Distance between probability distributions of discrete variables given samples

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

ddhellinger(x1, x2)

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.

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.

Returns

The distance between the two probability distributions.

Author(s)

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

See Also

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

Other distances: ddchisqsym, ddjeffreys, ddjensen, ddlp.

References

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

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)