gini {catsim} R Documentation

## Diversity Indices

### Description

`gini()` is a measure of diversity that goes by a number of different names, such as the probability of interspecific encounter or the Gibbs-Martin index. It is 1 - sum(p_i^2), where p_i is the probability of observing class i.

The corrected Gini-Simpson index, `ginicorr` takes the index and corrects it so that the maximum possible is 1. If there are `k` categories, the maximum possible of the uncorrected index is 1-1/k. It corrects the index by dividing by the maximum. `k` must be specified.

The modified Gini-Simpson index is similar to the unmodified, except it uses the square root of the summed squared probabilities, that is, 1 - √{ sum(p_i^2)}, where p_i is the probability of observing class i.

The modified corrected Gini index then corrects the modified index for the number of categories, `k`.

### Usage

```gini(x)

ginicorr(x, k)

sqrtgini(x)

sqrtginicorr(x, k)
```

### Arguments

 `x` binary or categorical image or vector `k` number of categories

### Value

The index (between 0 and 1), with 0 indicating no variation and 1 being maximal. The Gini index is bounded above by 1-1/k for a group with `k` categories. The modified index is bounded above by 1-1/√{k}. The corrected indices fix this by dividing by the maximum.

### Examples

```x <- rep(c(1:4), 5)
gini(x)

x <- rep(c(1:4), 5)
ginicorr(x, 4)

x <- rep(c(1:4), 5)
sqrtgini(x)

x <- rep(c(1:4), 5)
sqrtginicorr(x, 4)
```

[Package catsim version 0.2.3 Index]