# entropy

##### Normalized Shannon diversity index

A normalized Shannon vertical complexity index. The Shannon diversity index is a measure for quantifying diversity and is based on the number and frequency of species present. This index, developed by Shannon and Weaver for use in information theory, was successfully transferred to the description of species diversity in biological systems (Shannon 1948). Here it is applied to quantify the diversity and the evenness of an elevational distribution of las points. It makes bins between 0 and the maximum elevation. If there are negative values the function returns NA.

##### Usage

`entropy(z, by = 1, zmax = NULL)`

##### Arguments

- z
vector of positive z coordinates

- by
numeric. The thickness of the layers used (height bin)

- zmax
numeric. Used to turn the function entropy to the function VCI.

##### Value

A number between 0 and 1

##### References

Pretzsch, H. (2008). Description and Analysis of Stand Structures. Springer Berlin Heidelberg. http://doi.org/10.1007/978-3-540-88307-4 (pages 279-280) Shannon, Claude E. (1948), "A mathematical theory of communication," Bell System Tech. Journal 27, 379-423, 623-656.

##### See Also

##### Examples

```
# NOT RUN {
z = runif(10000, 0, 10)
# expected to be close to 1. The highest diversity is given for a uniform distribution
entropy(z, by = 1)
z = runif(10000, 9, 10)
# Must be 0. The lowest diversity is given for a unique possibility
entropy(z, by = 1)
z = abs(rnorm(10000, 10, 1))
# expected to be between 0 and 1.
entropy(z, by = 1)
# }
```

*Documentation reproduced from package lidR, version 2.0.0, License: GPL-3*