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When the sample mean is not the quantity of interest, other methods must be used. One can estimate the quantity of interest by studying the properties of the central sample moments: the sample skewness, the sample kurtosis, and the sample excess. For example, the sample mean and the sample skewness are correlated and higher skewness in a sample suggests a shift (or skew) on the right. One can use the properties of sample moments to deduce the properties of the distribution. See, for example, the book of An Introduction to Mathematical Statistics by Wilmott, Potter, Walker, and Westerback. d2c66b5586