Graduate A possible estimate for the fourth central moment

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The discussion centers on estimating the fourth central moment using kurtosis and standard deviation. It questions whether the fourth central moment can be approximated as the product of kurtosis and the standard deviation raised to the fourth power. Participants clarify that while skewness relates to the third central moment, the proposed relationship for the fourth moment may not be strictly defined. The conversation highlights the distinction between definitions and approximations in statistical moments. Overall, the thread explores the mathematical relationships between central moments, skewness, and kurtosis.
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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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