ddchisqsym function

Distance between probability distributions of discrete variables given samples

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

ddchisqsym(x1, x2)

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.

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.

Returns

The distance between the two probability distributions.

Author(s)

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

See Also

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

Other distances: ddhellinger, 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")
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)