ddlp {dad}

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)

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.

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.

Value

The distance between the two discrete probability distributions.

Author(s)

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

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)