I am currently looking into few static analyse algorithms. I noticed that they are analysing with different order moments or cumulants to analyse the data. I guess it is because these algorithms are focus on different aspect of the data itself.
So far as I know, 1st (mean) and 2nd(variance) moments are focus on the dispersion of the data as a whole, and 3rd moment (skewness) looks into the tail area of the distribution. 4th moment (kurtosis) concentrates on the peaks.
Can I then deduce that higher moments means the algorithm pays more attention to local static property?
Can anyone answer me explicitly to help me out of this headache? Or can you recommend some books or papers? I do extremely appreciate for your kind consideration and help.