I would like to prove that Skewness and Kurtosis are sufficient statistics for gaussian distribution.
Later on I will try to prove on loglogistic distribution.
Do you have any idea how to do that?
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Sign up to join this communityI would like to prove that Skewness and Kurtosis are sufficient statistics for gaussian distribution.
Later on I will try to prove on loglogistic distribution.
Do you have any idea how to do that?
You are going to fail --- you cannot prove what is not true!
More details: You obtain absolutely no information about the location of a Gaussian from the skewness or kurtosis. Proof: they are the same for a $\text{Normal}(\mu,\sigma)$ and $\text{Normal}(\mu′,\sigma)$ distribution, for any μ or μ′. Indeed, skewness is worthless, because it's always zero. (stated in comments by whuber).
As for the same question for loglogistic distribution, you would have to tell us why you expect skewness and kurtosis to be sufficient in that case (it is not).