catsim (version 0.2.4)

gini: 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, \(1 - \sqrt{ sum(p_i^2)}\), 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)

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 \(1-1/\sqrt{k}\). The corrected indices fix this by dividing by the maximum.

Arguments

x

binary or categorical image or vector

k

number of categories

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)