# The Gini coefficient adjusted for negative attributes (Raffinetti, Siletti and Vernizzi, 2015)

### Description

computes the Gini coefficient adjusted for negative (even weighted) data.

### Usage

1 | ```
Gini_RSV(y,w)
``` |

### Arguments

`y` |
a vector of attributes containing even negative elements |

`w` |
a vector containing the weights associated with the elements of the attribute vector |

### Details

`Gini_RSV(y,w)`

is the Gini coefficient for negative income data proposed by Raffinetti, Siletti and Vernizzi (2015) and based on a new
definition of the "polarized" scenario, where the total negative attribute amount is assigned to one unit, the total positive amount to another unit, while all
the other units have a zero amount of attribute. It provides a value always included into the close range [0,1].

### Value

the value of the Gini coefficient adjusted for negative attributes.

### Note

If the vector `w`

contains unitary elements, compute `Gini_RSV`

as `Gini_RSV(y)`

.

### Author(s)

Emanuela Raffinetti, Fabio Aimar

### References

E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS2014. 47th Scientific Meeting of the Italian Statistical Society", CUEC (Cooperativa Universitaria Editrice Cagliaritana), 11-13 June 2014

E. Raffinetti, E. Siletti, A. Vernizzi (2015), On the Gini coefficient normalization when incomes with negative values are considered, Statistical Methods & Applications, 24(3), 507-521

E. Raffinetti, E. Siletti, A. Vernizzi (2016), Analyzing the effects of negative and non-negative values on income inequality. Evidence from the Survey of Household Income and
Wealth of the Bank of Italy (2012), Social Indicators Research (published on line http://link.springer.com/article/10.1007

### See Also

`ineq`

,`IC2`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
# generate the vector of attributes with even negative elements
y<-c(-7,-15,11,-10,2,4,40)
# generate the vector of weights
w<-c(2.5,1.1,3.6,4.4,0.8,2.7,1.9)
# compute the Gini coefficient adjusted for negative values
Gini_RSV(y,w)
data(BI2012)
# define the vector of weights
w<-BI2012$weight
# select the vector of incomes (e.g., the incomes from transfers YTA)
y<-BI2012$YTA
# compute the Gini coefficient adjusted for negative values
Gini_RSV(y,w)
# select the vector of incomes (e.g., the incomes from financial capital gain YCF)
y<-BI2012$YCF
# compute the Gini coefficient adjusted for negative values
Gini_RSV(y,w)
``` |