What are the applications of higher order statistics?

[fisico30]

Hello Forum,

I am not clear on what higher order statistics actually mean. I know that if a process is Gaussian, it is fully described by its mean and variance. The higher order statistics are zero or redundant...IF the process is not Gaussian, then the HOS are useful...

1) How do we determine if a process is Gaussian first of all?
2) What type of operations do we mean with higher order statistics?

thanks
fisico30

 

[John Creighto]

Hello Forum,

I am not clear on what higher order statistics actually mean. I know that if a process is Gaussian, it is fully described by its mean and variance. The higher order statistics are zero or redundant...IF the process is not Gaussian, then the HOS are useful...

1) How do we determine if a process is Gaussian first of all?
2) What type of operations do we mean with higher order statistics?

thanks
fisico30

Skewness, which is the third central moment determines how symetric a distribution is. The four central moment Kurtosis determines how tail heavy a distribution. If a distribution is more tail heavy then there is greater variance in estimating the mean. There are formal statistics test for testing how well a process fits a given random distribution. However, you can get some idea of what kind of distiribution might make a good fit just by plotting a histogram.