Langel, Matti

2013, Langel, Matti, Tillé, Yves

Since Corrado Gini suggested the index that bears his name as a way of measuring inequality, the computation of variance of the Gini index has been subject to numerous publications. In this paper, we survey a large part of the literature related to the topic and show that the same results, as well as the same errors, have been republished several times, often with a clear lack of reference to previous work. Whereas existing literature on the subject is very fragmented, we regroup papers from various fields and attempt to bring a wider view of the problem. Moreover, we try to explain how this situation occurred and the main issues involved when trying to perform inference on the Gini index, especially under complex sampling designs. The interest of several linearization methods is discussed and the contribution of recent papers is evaluated. Also, a general result to linearize a quadratic form is given, allowing the approximation of variance to be computed in only a few lines of calculation. Finally, the relevance of the regression-based approach is evaluated and an empirical comparison is proposed.

2011-8, Langel, Matti, Tillé, Yves

2010-2, Langel, Matti, Tillé, Yves

2009-2, Langel, Matti, Tillé, Yves

2012-10-1, Tillé, Yves, Langel, Matti

In grouped data, the estimation of the Lorenz curve without taking into account the within-class variability leads to an overestimation of the curve and an underestimation of the Gini index. We propose a new strictly convex estimator of the Lorenz curve derived from a linear interpolation-based approximation of the cumulative distribution function. Integrating the Lorenz curve, a correction can be derived for the Gini index which takes the intra-class variability into account.

2011-2, Langel, Matti, Tillé, Yves

2009-11, Langel, Matti, Tillé, Yves

2011-8, Antal, Erika, Langel, Matti, Tillé, Yves

2010-2, Langel, Matti, Tillé, Yves

2009-8, Langel, Matti, Tillé, Yves