OnomasticDiversity (version 0.1)

fCressieRead: Cressie and Read

Description

This function obtains the Cressie and Read statistics introduced by Noel Cressie and Timothy Read. It is a method for quantifying species biodiversity that can be adapted to the context of onomastics.

Usage

fCressieRead(x, number, population, ni, location, lambda)

Value

A dataframe containing the following components:

location

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

cressieRead

the value of Cressie and Read statistics.

Arguments

x

dataframe of the data values.

number

name of a variable which represents number of individuals of each species.

population

name of variable which represents total number of individuals.

ni

name of variable which represent number of species.

location

name of variable which represent represents the grouping element.

lambda

free parameter.

Author

Maria Jose Ginzo Villamayor

Details

For a community \(i\), Cressie and Read (1984) introduced the following parametric form for a generalised statistic \(I_n (\lambda) = \frac{2}{\lambda(\lambda+1)} \sum_{k\in S_i} { n_{ki} \left[ \left(\frac{n_{ki}}{n/S_i}\right)^\lambda-1\right]}\), where \(n_{ki}\) represents the number of individuals of species \(k\) in a sample (in the population is \(N_{ki}\)), \(S_i\) represents all species at the community, species richness, and \(\lambda\) is a free parameter.

Varying the value of \(\lambda\) gets different statistics. If \(\lambda= -1\) and \(\lambda= 0\), \(I_n(\lambda)\) is not defined, but in any case, limits \(\lambda = -1\) and \(\lambda = 0\) can be taken.

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

References

Cressie, Noel and Read, Timothy RC (1984) Multinomial goodness-of-fit tests. Computational Statistics and Data Analysis, 46(3), 440--464.

See Also

fHill

Examples

data(surnamesgal14)
result = fCressieRead(x= surnamesgal14 , number="number",
population="population", location = "muni", ni="ni",
lambda = 2)
result