kurtosis & skewness

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kurtosis kurtosis is a measure of the “tailedness” of the probability distribution of a real-valued random variable. The standard measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population. This number is related to the tails of the distribution, not its peak;hence, the sometimes-seen characterization as “peakedness” is mistaken. For this measure, higher kurtosis is the result of infrequent extreme deviations (or outliers), as opposed to frequent modestly sized deviations. 在相同的标准差下，峰度系数越大，分布就有更多的极端值，那么其余值必然要更加集中在众数周围，其分布必然就更加陡峭。

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skewness In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or undefined. For a unimodal distribution(单峰分布), negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right.

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