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

 ddjeffreys R Documentation

## Divergence between probability distributions of discrete variables given samples

### Description

jeffreys's divergence (symmetrized Kullback-Leibler divergence) between two multivariate (`q > 1`) or univariate (`q = 1`) discrete probability distributions, estimated from samples.

### Usage

``````ddjeffreys(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 jeffreys's divergence between the discrete probability distributions of the samples are computed using the `ddjeffreyspar` function.

### Value

The divergence between the two 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.

`ddjeffreyspar`: Jeffrey's distances between two discrete distributions, given the probabilities on their common support.

Other distances: `ddchisqsym`, `ddhellinger`, `ddjensen`, `ddlp`.

### Examples

``````# Example 1
x1 <- c("A", "A", "B", "B")
x2 <- c("A", "A", "A", "B", "B")
ddjeffreys(x1, x2)

# Example 2 (Its value can be infinity -Inf-)
x1 <- c("A", "A", "B", "C")
x2 <- c("A", "A", "A", "B", "B")
ddjeffreys(x1, x2)

# Example 3
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")))
ddjeffreys(x1, x2)
``````

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