Concentration Measures

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

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.

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.

Value

the value of the concentration measure

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.

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.

Author

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

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)
#> [1] 0.1840812

# compute coefficient of Hall/Tiedemann/Rosenbluth
Rosenbluth(x)
#> [1] 0.1859051

# Some more examples
Herfindahl(c(261,29,33,15,39,28,95,5,6,28,69,8,105,38,15))
#> [1] 0.1668737
Herfindahl(c(783,121,112,70,201,153,425,19,37,126,325,51,442,193,41))
#> [1] 0.1301292