R: Concentration Measures

Herfindahl {DescTools} | R Documentation

## Concentration Measures

### Description

Computes the concentration within a vector according to the specified concentration measure.

### Usage

    Herfindahl(x, n = rep(1, length(x)), parameter = 1, na.rm = FALSE)
    Rosenbluth(x, n = rep(1, length(x)), na.rm = FALSE)

### Arguments

`x` | a vector containing non-negative elements
`n` | a vector of frequencies (weights), must be same length as x.
`parameter` | parameter of the concentration measure (if set to `NULL` the default parameter of the respective measure is used)
`na.rm` | logical. Should missing values be removed? Defaults to FALSE.

### Value

the value of the concentration measure

### Note

The same measure is usually known as the Simpson index in ecology, and as the Herfindahl index or the Herfindahl-Hirschman index (HHI) in economics.

### Note

These functions were previously published as `conc()` in the ineq package and have been integrated here without logical changes. `NA` and weights support were added.

### Author(s)

Achim Zeileis <achim.zeileis@r-project.org>

### References

Cowell, F. A. (2000) Measurement of Inequality, in Atkinson, A. B., Bourguignon, F. Handbook of Income Distribution. (Eds) Amsterdam

Cowell, F. A. (1995) Measuring Inequality. Prentice Hall/Harvester Wheatshef

Hall, M., Tidemann, N. (1967) Measures of Concentration, JASA 62, 162-168.

### See Also

See `Gini`, `Atkinson` and `ineq()` for additional inequality measures

### Examples

    # generate vector (of sales)
    x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)

    # compute Herfindahl coefficient with parameter 1
    Herfindahl(x)

    # compute coefficient of Hall/Tiedemann/Rosenbluth
    Rosenbluth(x)

    # Some more examples
    Herfindahl(c(261,29,33,15,39,28,95,5,6,28,69,8,105,38,15))
    Herfindahl(c(783,121,112,70,201,153,425,19,37,126,325,51,442,193,41))

[Package DescTools version 0.99.35 Index]