# kullback_leibler_divergence: Kullback-Leibler divergence In kylebittinger/abdiv: Alpha and Beta Diversity Measures

## Description

Kullback-Leibler divergence

## Usage

 `1` ```kullback_leibler_divergence(x, y) ```

## Arguments

 `x, y` Numeric vectors representing probabilities

## Details

Kullback-Leibler divergence is a non-symmetric measure of difference between two probability vectors. In general, KL(x, y) is not equal to KL(y, x).

Because this measure is defined for probabilities, the vectors x and y are normalized in the function so they sum to 1.

## Value

The Kullback-Leibler divergence between `x` and `y`. We adopt the following conventions if elements of `x` or `y` are zero: 0 \log (0 / y_i) = 0, 0 \log (0 / 0) = 0, and x_i \log (x_i / 0) = ∞. As a result, if elements of `x` are zero, they do not contribute to the sum. If elements of `y` are zero where `x` is nonzero, the result will be `Inf`. If either `x` or `y` sum to zero, we are not able to compute the proportions, and we return `NaN`.

kylebittinger/abdiv documentation built on Jan. 31, 2020, 3:13 p.m.