Redefinition of Skew Distribution

• 1、Riztec Research Institute, Zhongshan City, Guangdong Province

Abstract：The asymmetry of skew distribution makes the position characteristic parameter not equal to the average value. The expected value, as the position characteristic parameter of normal distribution, is equal to the average value, which is determined by its symmetrical nature. Of the position characteristic parameters of asymmetric skew distribution, only peak value can be valued at the maximum value point of the distribution curve, which determines that there is no expected value for skew distribution. In the case of asymmetry, the inflexion of the single increasing function on the left side and the single decreasing function on the right side of the peak must be asymmetric, which leads to different discrete characteristic parameters of random variables on the left and right sides of the peak. The position characteristic parameter of normal distribution is expected value or peak value, which is equal to average value. However, only peak value is the position characteristic parameter of skew distribution and it is not equal to the average value, which makes the expected value disappear. The discrete characteristic parameters that are unique to skew distribution and completely different from normal distribution need to be re normalized, and skew distribution needs to be redefined.

Keywords： skew distribution position characteristic parameter discrete characteristic parameter peak value peak variance peak deviation