Understanding Standardized Cumulants in the Edgeworth Series

[jostpuur]

http://en.wikipedia.org/wiki/Edgeworth_series

...and standardized cumulants \gamma_r.

What does "standardized cumulant" mean? It becomes clear in the context that it is something different from the ordinary cumulant, but how has it been altered?

 

[SW VandeCarr]

http://en.wikipedia.org/wiki/Edgeworth_series
What does "standardized cumulant" mean? It becomes clear in the context that it is something different from the ordinary cumulant, but how has it been altered?

Cumulants \kappa_{r} have a direct relationship to moments.

\kappa_{1} = \mu_{1}

\kappa_{2} = \mu_{2}-\mu_{1}^2

The is mean is 0 and the variance is 1 for the standard normal distribution.