OnomasticDiversity (version 0.1)

fSimpsonInf: Calculate the Simpson's diversity index and the inverse

Description

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

Usage

fSimpsonInf(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.

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 (when \(N_i\) is not finite, data are assumed to come from a sample of size \(N_i\)) diversity index is defined by \(D^{\prime}_{S_i} = \sum \limits_{k\in S_i} \frac{n_{ki}(n_{ki}-1)}{n_i(n_i-1)}\), where \(n_{ki}\) represents the number of individuals of species \(k\) in a sample (in the total is \(N_{ki}\)) and \(S_i\) represents all species at the community, species richness.

In onomastic context, \(n_{ki}\) (\(\approx N_{ki}\)) denotes the absolute frequency of surname \(k\) in region \(i\) and \(S_i\) are all surnames in region (\(\approx\) community diversity context) \(i\).

References

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

See Also

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

Examples

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

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

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