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annaphys
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And why does it matter if they are extensive or not?
Cumulants and moments are statistical measures used to describe the shape and distribution of a set of data. Moments are calculated using the raw data values, while cumulants are calculated using the moments.
Cumulants are extensive because they scale linearly with the size of the data set. This means that as the number of data points increases, the cumulants also increase proportionally.
Moments are not extensive because they are affected by the scale of the data set. As the number of data points increases, the moments may not increase proportionally, and can even approach a limit or converge to a specific value.
Extensivity in cumulants and moments is important because it allows for a more accurate and consistent comparison of data sets of different sizes. By using extensive measures, we can better understand the underlying distribution of the data and make meaningful comparisons.
Cumulants and moments are commonly used in fields such as physics, chemistry, and economics to analyze and compare data sets. They can provide valuable insights into the properties and behavior of complex systems, and are often used in statistical modeling and forecasting.