kurtosis
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Kurtosis (from ( or ), meaning 'curved, arching') refers to the degree of tailedness in the probability distribution of a real-valued, random variable in probability theory and statistics. Similar to skewness, kurtosis provides insight into specific characteristics of a distribution. Various methods exist for quantifying kurtosis in theoretical distributions, and corresponding techniques allow estimation based on sample data from a population. Different measures of kurtosis can yield varying interpretations.
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~24 min read
Article
26 sectionsContents
- Pearson moments
- Interpretation
- Moors' interpretation
- Maximal entropy
- Excess kurtosis
- Mesokurtic
- Leptokurtic
- Platykurtic
- Graphical examples
- The Pearson type VII family
- Other well-known distributions
- Sample kurtosis
- Definitions
- A natural but biased estimator
- Standard unbiased estimator
- Upper bound
- Variance under normality
- Applications
- Kurtosis convergence
- Seismic signal analysis
- Weather prediction
- Other measures
- See also
- References
- Further reading
- External links
Kurtosis (from ( or ), meaning 'curved, arching') refers to the degree of tailedness in the probability distribution of a real-valued, random variable in probability theory and statistics. Similar to skewness, kurtosis provides insight into specific characteristics of a distribution. Various methods exist for quantifying kurtosis in theoretical distributions, and corresponding techniques allow estimation based on sample data from a population. Different measures of kurtosis can yield varying interpretations.
The standard measure of a distribution's kurtosis, originating with Karl Pearson, is a scaled version of the fourth moment of the distribution. This number is related to the tails of the distribution, not its peak; hence, the sometimes-seen characterization of kurtosis as peakedness is incorrect. For this measure, higher kurtosis corresponds to greater extremity of deviations (or outliers), and not the configuration of data near the mean.