Abstract
Gini’s Mean Difference (GMD) and the Gini index are widely applied tools in statistics. The Gini concentration index is one of the most common statistical indices employed in the social sciences for measuring concentration in the distribution of a positive random variable. This chapter describes how the GMD can be used for testing the data on positive correlation. It aims to analyze the behavior of the GMD for correlated random variables. Of course, it would be interesting to monitor not only the correlation structure but also the mean and the variability behavior of the data at once. The GMD has also been applied in survival analysis, while the Gini concentration index has been used to describe concentration in levels of mortality and length of life among different socioeconomic groups, and to evaluate inequality in health and life expectancy. The chapter shows how control charts based on the GMD can be constructed to monitor the correlation structure of a process.
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