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)
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 |
na.rm |
logical. Should missing values be removed? Defaults to FALSE. |
the value of the concentration measure
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.
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.
Achim Zeileis <achim.zeileis@r-project.org>
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.
# 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))
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