Q-Theil指数
Introducing the q-Theil index
摘要：
从Tsallis关于非广延统计力学的思想和{ \it q-熵}的概念出发，我们回忆了Theil指数$Th$，并将其转化为$Th_q$指数.这两个指数都可以用来以非线性的方式将任何时间序列映射到自己身上。我们将$Th_q$应用于20个富裕国家在1950 - 2003年期间的GDP演变，并寻求其经济全球化的证据。首先，我们计算“新的”时间序列和它们的平均值之间的距离，从这些数据构造简单的网络。我们强调，考虑不同的时间“参数”是有用的，我们也确实考虑了不同的时间“参数”：（i）原始时间序列计算$Th_q$指数的移动平均时间窗口;（ii）计算时间序列距离的移动平均时间窗口;（iii）相关时间滞后。这使我们能够推断出最佳条件来衡量网络的特征，即1970年出现的全球化进程在这些国家的经济和目前开始偏离。此处使用的$q$值是测量总数据分布的值，等于1.8125。
英文摘要：
Starting from the idea of Tsallis on non-extensive statistical mechanics and the {\it q-entropy} notion, we recall the Theil index $Th$ and transform it into the $Th_q$ index. Both indices can be used to map onto themselves any time series in a non linear way. We develop an application of the $Th_q$ to the GDP evolution of 20 rich countries in the time interval [1950 - 2003] and search for a proof of globalization of their economies. First we calculate the distances between the "new" time series and to their mean, from which such data simple networks are constructed. We emphasize that it is useful to, and we do, take into account different time "parameters": (i) the moving average time window for the raw time series to calculate the $Th_q$ index; (ii) the moving average time window for calculating the time series distances; (iii) a correlation time lag. This allows us to deduce optimal conditions to measure the features of the network, i.e. the appearance in 1970 of a globalization process in the economy of such countries and the present beginning of deviations. The $q$ value hereby used is that which measures the overall data distribution and is equal to 1.8125.
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