Atkinson {DescTools} | R Documentation |

## Atkinson Index - A Measure of Inequality.

### Description

The Atkinson index is an inequality measure and is useful in determining which end of the distribution contributed most to the observed inequality.

### Usage

```
Atkinson(x, n = rep(1, length(x)), parameter = 0.5, na.rm = FALSE)
```

### Arguments

`x` |
a vector containing at least non-negative elements. |

`n` |
a vector of frequencies, must be same length as x. |

`parameter` |
parameter of the inequality measure (if set to |

`na.rm` |
logical. Should missing values be removed? Defaults to FALSE. |

### Value

the value of the Akinson Index.

### Note

This function was previously published as `ineq()`

in the ineq package and has been
integrated here without logical changes, but with some extensions for `NA`

-handling and the use of weights.

### Author(s)

Achim Zeileis <Achim.Zeileis@R-project.org>

### References

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

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

Marshall, Olkin (1979) *Inequalities: Theory of Majorization and Its
Applications*. New York: Academic Press.

Atkinson, A. B. (1970): On the Measurment of Inequality, *Journal of Economic Theory*, Vol. 2(3), pp. 244-263.

### See Also

See `Herfindahl`

, `Rosenbluth`

for concentration measures and
`ineq()`

in the package ineq for additional inequality measures

### Examples

```
# generate vector (of incomes)
x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
# compute Atkinson coefficient with parameter=1
Atkinson(x, parameter=1)
```

*DescTools*version 0.99.55 Index]