OnomasticDiversity (version 0.1)

fSimpson: Calculate the Simpson's diversity index

Description

This function obtains the Simpson's diversity index and the inverse introduced by Edward Hugh Simpson. It was the first index used in ecology. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fSimpson(x, k, n, location)

Value

A dataframe containing the following components:

location

represents the grouping element, for example the communities / regions.

simpson

the value of the Simpson's diversity index.

divSimpson

the value of the inverse Simpson's diversity index.

Arguments

x

dataframe of the data values for each species.

k

name of a variable which represents absolute frequency for each species

n

name of a variable which represents total number of individuals.

location

represents the grouping element.

Author

Maria Jose Ginzo Villamayor

Details

For a community \(i\), the Simpson's diversity index is defined by \(D_{S_i} = \sum \limits_{k\in S_i} p_{ki}^2\), where \(p_{ki}\) represents the relative frequency of species \(k\), because \(p_{ki} = \frac{N_{ki}}{N_i}\), (where \(N_{ki}\) denotes the number of individuals of species \(k\) and \(N_i\) total number of individuals in all \(S_i\) species at the community, species richness. The Simpson index tends to be smaller when the community is more diverse.

In onomastic context, \(p_{ki}\) denotes the relative frequency of surname \(k\) in region (\(\approx\) community diversity context) \(i\), i.e., Simpson's diversity index is equivalent to the concept of isonymy..

References

Simpson (1949) Measurement of diversity. Nature, 163.

See Also

fMargalef, fMenhinick, fPielou, fShannon, fSheldon, fSimpsonInf, fGeneralisedMean, fGeometricMean, fHeip.

Examples

data(surnamesgal14)
result = fSimpson (x= surnamesgal14, k="number",
n="population", location  = "muni" )
result

data(namesmengal16)
result = fSimpson (x= namesmengal16, k="number",
n="population", location  = "muni" )
result

data(nameswomengal16)
result = fSimpson (x= nameswomengal16, k="number",
n="population", location  = "muni" )
result