A possible estimate for the fourth central moment

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SUMMARY

The discussion centers on estimating the fourth central moment in statistics, specifically questioning whether it can be defined as the product of kurtosis and the standard deviation raised to the fourth power. Participants clarify that while the third central moment is indeed the product of skewness and the standard deviation raised to the third power, the fourth central moment's relationship with kurtosis is more complex. The consensus is that this formulation is not merely an approximation but a fundamental definition in statistical analysis.

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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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I thought that was the definition of skewness/ the third central moment, not an approximation.
 

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