A possible estimate for the fourth central moment

In summary, the fourth central moment, also known as kurtosis, is a measure of the shape of a probability distribution. It is important because it provides information about the distribution's symmetry and tail heaviness, which can help identify outliers and anomalies. The fourth central moment is calculated by taking the average of the fourth power of deviations from the mean. A positive or negative value indicates a peaked or flatter distribution, respectively, with a value of 0 indicating a normal distribution. It can be used to compare different distributions, but data should be standardized before making comparisons.
  • #1
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TL;DR Summary
A possible estimate for the third central moment is the product of the skewness and the standard deviation raised to the third power. Is it also true that a possible estimate for the fourth central moment is the product of the kurtosis and the standard deviation raised to the fourth power?
A possible estimate for the third central moment is the product of the skewness and the standard deviation raised to the third power. Is it also true that a possible estimate for the fourth central moment is the product of the kurtosis and the standard deviation raised to the fourth power?
 
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  • #2
I thought that was the definition of skewness/ the third central moment, not an approximation.
 

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