Statistics
Kurtosis
A measure of the tailedness or likelihood of extreme outliers in a distribution compared to a normal distribution.
What is Kurtosis?
Kurtosis describes the shape of a distribution's tails in relation to its peak. High kurtosis indicates heavy tails and a sharp peak, meaning data has more extreme outliers. Low kurtosis indicates light tails and a flatter peak.
Why Kurtosis Matters
Kurtosis helps researchers understand the risk of extreme, rare events in their data, which can heavily leverage statistical models.
Example
Financial returns often exhibit high kurtosis; most days show small changes, but occasionally there are massive market crashes or surges.
Common Mistakes
- Historically, teaching that kurtosis measures the peakedness of the center of the distribution, when mathematically it primarily measures the weight of the tails.
- Ignoring high kurtosis when running regressions, leaving models vulnerable to being skewed by outliers.