dad (version 4.1.6)

ddlp: Distance between probability distributions of discrete variables given samples

Description

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

Usage

ddlp(x1, x2, p = 1)

Value

The distance between the two discrete probability distributions.

Arguments

x1, x2

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

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

p

integer. Parameter of the distance.

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 \(L^p\) distance between the discrete probability distributions of the samples are computed using the ddlppar function.

References

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

See Also

ddlppar: \(L^p\) distance between two discrete distributions, given the probabilities on their common support.

Other distances: ddchisqsym, ddhellinger, ddjeffreys, ddjensen.

Examples

# Example 1
x1 <- c("A", "A", "B", "B")
x2 <- c("A", "A", "A", "B", "B")
ddlp(x1, x2)
ddlp(x1, x2, p = 2)

# 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")))
ddlp(x1, x2)