...and standardized cumulants [itex]\gamma_r[/itex].
jostpuur said: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?
Standardized cumulants are statistical measures used to describe the shape of a probability distribution. They are calculated from the moments of the distribution and are used to compare different distributions or to identify patterns in data.
To calculate standardized cumulants, you first need to calculate the moments of the distribution. Then, the standardized cumulants are calculated by dividing the moments by the appropriate power of the standard deviation of the distribution.
The purpose of using standardized cumulants is to compare different distributions or to identify patterns in data. They provide a standardized measure that can be used to compare distributions with different scales or units.
One limitation of using standardized cumulants is that they only provide information about the shape of the distribution and do not take into account other characteristics such as the mean or variance. Additionally, they may not accurately capture the shape of distributions with heavy tails or outliers.
Standardized cumulants are commonly used in fields such as physics, engineering, and finance to analyze data and make comparisons between different distributions. They can also be used to identify patterns or trends in data, such as in time series analysis or in the study of complex systems.