# ddlp: Distance between probability distributions of discrete... In dad: Three-Way / Multigroup Data Analysis Through Densities

 ddlp R Documentation

## 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.

`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)
``````

dad documentation built on Aug. 30, 2023, 5:06 p.m.