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 |

`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))
```

*DescTools*version 0.99.55 Index]