In the context of Social Welfare and Choquet integration, we briefly review, on the one hand, the generalized Gini welfare functions and inequality indices for populations of n ≥ 2 individuals, and on the other hand, the Möbius representation framework for Choquet integration, particularly in the case of k-additive symmetric capacities. We recall the binomial decomposition of OWA functions due ...

BACKGROUND & AIM While most of the published researches have reported the amount of inequity in geographical distribution of important health resources, only a small number of studies have focused on the trend of inequality in the distribution of these resources. The purpose of this study was to determine the trend of inequality in the distribution of intensive care beds in Iran during 2010 to ...

background: inequality in households’ and individuals' consumption expenditures is one of the most important aspects of health status difference among households and individuals. objectives: we investigated the impact of some macro-economic factors specially inequality factors on the iranian rural health status since 1986 through 2012. patients and methods: we conducted a longitudinal ecologica...

This paper proposes and proves the important equivalence between the Gini index and the area under the Kolmogorov-Smirnov (KS) distribution curve. The proof’s rationale is similar to that used in the proof of equivalence between AUC_ROC and AUC_KS. But different from that, this one uses a transformation that preserves the 1-to-1 correspondence between the ideal classifier on the KS and Lorenz c...

Morton Paglin recently proposed a new summary statistic~ the "Paglin-Gini," which he uses to measure an.d analyze the level and trend of income inequality in the United States. In contrast with the standard Lorenz-Gini, which counts all income differences among living units in measuring inequality, the Paglin-Gini defines meaningful inequality to include only the differences in family incomes t...

The spatial scan statistic is an important tool for spatial cluster detection. There have been numerous studies on scanning window shapes. However, little research has been done on the maximum scanning window size or maximum reported cluster size. Recently, Han et al. proposed to use the Gini coefficient to optimize the maximum reported cluster size. However, the method has been developed and e...

Spatial scan statistics with circular or elliptic scanning windows are commonly used for cluster detection in various applications, such as the identification of geographical disease clusters from epidemiological data. It has been pointed out that the method may have difficulty in correctly identifying non-compact, arbitrarily shaped clusters. In this paper, we evaluated the Gini coefficient fo...

In text classification, the purity of the Gini index can be used. When purity value is greater, the characteristic of the information contained in the attribute is higher, and the feature distinguishing capability is stronger. But using the Gini purity formula on feature weight, the classification result is not very good, one of the main reasons is those rare words only appearing in one categor...

In diagnostic decision-support systems, test selection amounts to selecting, in a sequential manner, a test that is expected to yield the largest decrease in the uncertainty about a patient’s diagnosis. For capturing this uncertainty, often an information measure is used. In this paper, we study the Shannon entropy, the Gini index, and the misclassification error for this purpose. We argue that...

We correct a proof given in [1] for the one-parameter family of Gini means, and point out general remarks on the general Gini means. 2000 Mathematical Subject Classification: 26D15, 26D99