# Decomposition by Groups for Atkinson Index

### Description

Decomposes by population subgroups an Atkinson measure of inequality within a vector.

### Usage

1 | ```
decompAtkinson(x, z, w = NULL, epsilon = 1, decomp = "BDA", ELMO = TRUE)
``` |

### Arguments

`x` |
Numeric vector with non-negative values (strictly positive
when |

`z` |
Factor who determines the subgroups. |

`w` |
Numeric vector of sampling weigths (optional). |

`epsilon` |
Parameter of the Atkinson index (must be strictly positive). |

`decomp` |
Character string specifying the decomposition. It must be one of |

`ELMO` |
When |

### Value

A list of class `"ICI"`

with components:

`ineq` |
a list with components |

`decomp` |
a list with components |

`intra` |
a list with component |

`ws` |
a list with components |

`nas` |
a list with |

### References

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

Blackorby C., Donaldson D., Auersperg M. (1981) A new procedure for the
measurement of inequality within and among population subgroups. *Canadian
Journal of Economics*, 14, pp. 665-685.

Das T., Parikh A. (1982) Decomposition of Inequality Measures and a
Comparative Analysis. *Empirical Economics*, 7(1-2), pp. 23-48.

Elbers C., Lanjouw P., Mistiaen J.A., Ozler B. (2005)
*Re-Interpreting
Sub-Group Inequality Decompositions*. World Bank, World Bank Policy Research
Working Paper 3687, 42 p.

### See Also

`calcAtkinson`

### Examples

1 2 3 4 5 6 | ```
data(hhbudgets)
decompAtkinson(hhbudgets[,"ingreso"], hhbudgets[,"estructura"], epsilon=3)
summary(hhbudgets[,"tenencia"]) # 35 NA's
summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", ELMO=FALSE))
summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", epsilon=0.25))
``` |