Excess kurtosis

From Bogleheads
Jump to navigation Jump to search
Kurtosis

Kurtosis is a measure of whether the data in a data set are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers.[1]

In computing kurtosis the formula used is μ4/σ4 where μ4 is Pearson’s fourth moment about the mean and sigma is the standard deviation.

The normal distribution (Gaussian) is found to have a kurtosis of three. The formula μ4/σ4 - 3 is the formula for excess kurtosis. We could then classify a distribution from its excess kurtosis:

  • Mesokurtic distributions have excess kurtosis of zero.
  • Platykurtic distributions (light tails) have negative excess kurtosis.
  • Leptokurtic distributions (heavy tails) have positive excess kurtosis.[2]

The mathematical formulas used in google/excel spreadsheet statistical functions that are used in wiki statistical spreadsheets:

  • SKEW
  • KURT

Skew-kurtosis.gif

See also

References

  1. Measures of Skewness and Kurtosis, Engineering Statistics Handbook
  2. What Is Kurtosis? About education

External links