论文标题
皮尔逊偏度的新生活
A new life of Pearson's skewness
论文作者
论文摘要
在这项工作中，我们展示了如何成功地将耦合和随机优势方法应用于严格的皮尔逊偏度的经典问题。在这里，我们使用Fréchet手段来定义我们称为真正积极和真正负面的积极和消极偏度的广义观念。然后，我们在确定连续随机变量是否真正呈阳性的标准中采用随机优势方法。直觉上，这意味着概率密度函数的右尾缩放的尾巴在等效尺度的左尾部表现出严格的随机优势。最后，我们使用随机优势标准，并建立了一些真正积极偏度的基本示例，从而证明了该方法的一般方式。
In this work we show how coupling and stochastic dominance methods can be successfully applied to a classical problem of rigorizing Pearson's skewness. Here, we use Fréchet means to define generalized notions of positive and negative skewness that we call truly positive and truly negative. Then, we apply stochastic dominance approach in establishing criteria for determining whether a continuous random variable is truly positively skewed. Intuitively, this means that scaled right tail of the probability density function exhibits strict stochastic dominance over equivalently scaled left tail. Finally, we use the stochastic dominance criteria and establish some basic examples of true positive skewness, thus demonstrating how the approach works in general.
