# Computing the Gini-Based Coefficients for Weighted and Negative Attributes

### Description

This package was born to extend the Gini-based coefficients to non-traditional scenarios, i.e. in the case of negative data. The computation of the Gini coefficient in the case of negative weighted data involves, in addition to the vector of attributes (typically incomes), the vector of weights associated with each statistical unit. Two functions are made available for the computation of the Gini coefficient in the case of negative attributes. A first function is based on the contribution by Chen, Tasur and Rhai (1982), further improved by Berebbei and Silber (1985). Recently, a more appropriate normalization factor was introduced by Raffinetti, Siletti and Vernizzi (2015), who specified a new definition of the "polarized" scenario, where the total negative attribute amount is assigned to one unit, the total positive attribute amount to another unit, while all the other units have a zero amount of attribute. Also the plot of the corresponding curve of maximum inequality (RSV curve), both by considering the attribute values in absolute and relative terms, is provided. Moreover, even the function for the computation of the pseudo-Gini (concentration) coefficient is given, as proposed by Raffinetti, Siletti and Vernizzi (2016).

### Details

Package: | GiniWegNeg |

Type: | Package |

Version: | 1.0.1 |

Date: | 2016-05-20 |

License: | GPL-3 |

### Author(s)

Emanuela Raffinetti, Fabio Aimar

Maintainer: Emanuela Raffinetti <emanuela.raffinetti@unimi.it>

### References

C.N. Chen, T.W. Tsaur, T.S. Rhai (1982), The Gini coefficient and negative income, Oxford Economic Papers 34, 473–478

Z.M. Berrebi, J. Silber (1985), The Gini coefficient and negative income: a comment, Oxford Economic Papers 37, 525–526

E. Raffinetti, E. Siletti, A. Vernizzi (2014), Inequality measures and the issue of negative income. Italian Statistical Society Conference (SIS), Book of Short Papers: "SIS 2014. 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

`Gini_CTR_BS`

, `Gini_RSV`

, `GRSVc`

, `PGini_RSV`

, `RSVc`