The Representative Points of Nonlinear Transformation of Random Variable
Mengwen Cheng, Shuhe Lei · 2021
In this paper, we study the RPs of the nonlinear transformation of random variable under the mean-squared errors criterion. We explore the RPs of exponential distribution and uniform distribution, lognormal distribution and standard normal distribution, standard normal distribution and Chi-square distribution. We find that the RPs following the similar transformation of random variable have almost certain ralations. When the number of RPs is large, this relationship is consistent with that between variables, and some parameters may be slightly different. The existing methods to calculate the RPs of distributions have the defect of huge amount of calculation. By exploring the relationship between RPs of distributions, we can find a new method to calculate the RPs of distributions and avoid the defects of existing methods.