gini {catsim} | R Documentation |
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
.
gini(x)
ginicorr(x, k)
sqrtgini(x)
sqrtginicorr(x, k)
x |
binary or categorical image or vector |
k |
number of categories |
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.
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)