![]() ![]() It is also common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the standard normal distribution. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution. Distributions with kurtosis greater than 3 are said to be leptokurtic. An example of a platykurtic distribution is the uniform distribution, which does not produce outliers. Rather, it means the distribution produces fewer and less extreme outliers than does the normal distribution. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is "flat-topped" as is sometimes stated. It is common to compare the kurtosis of a distribution to this value. The kurtosis of any univariate normal distribution is 3. For this measure, higher kurtosis corresponds to greater extremity of deviations (or outliers), and not the configuration of data near the mean. This number is related to the tails of the distribution, not its peak hence, the sometimes-seen characterization of kurtosis as "peakedness" is incorrect. The standard measure of a distribution's kurtosis, originating with Karl Pearson, is a scaled version of the fourth moment of the distribution. Different measures of kurtosis may have different interpretations. ![]() Like skewness, kurtosis describes the shape of a probability distribution and there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. ![]()
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