Darmois–Skitovich_theorem
Darmois–Skitovich theorem
If 2 linear forms on independent random variables are independent, the variables are normal
In mathematical statistics, the Darmois–Skitovich theorem characterizes the normal distribution (the Gaussian distribution) by the independence of two linear forms from independent random variables. This theorem was proved independently by G. Darmois and V. P. Skitovich in 1953.[1][2]