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Kurtosis

Kurtosis

Kurtosis is a statistical measure that describes the shape of the distribution of a dataset, specifically focusing on the tails and the peak of the distribution. It provides insights into the likelihood of extreme values occurring in the data set compared to a normal distribution.

Definition and Interpretation

Kurtosis is often described by two main types:

Formula

The formula for sample kurtosis is:

kurtosis = (1/n) * (sum((x_i - mean)^4) / (standard deviation)^4) - 3

Where:

History

The concept of kurtosis was introduced by Karl Pearson in the early 20th century. Pearson, a prominent figure in statistics, used the term to describe the "peakedness" of the distribution. However, over time, the focus shifted from peakedness to the tails of the distribution due to theoretical and practical considerations.

Applications

Limitations

References

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