Thursday, July 9, 2015

'Student', on Kurtosis

W. S. Gosset (Student) provided this useful aid to help us remember the difference between platykurtic and leptokurtic distributions:

('Student', 1927. Errors of routine analysis. Biometrika, 19, 151-164. See p. 160.)

Here, β2 is the fourth standardized moment of the distribution about its mean. The Normal distribution has β2 = 3.

The appropriate definition of "kurtosis" for uni-modal distributions has been the subject of considerable discussion in the statistical literature. Should it be based on the characteristics of the tail of the distribution; the shape of the density around its mode; or both? 

© 2015, David E. Giles


  1. Tails only. You can easily have "platy" distributions that have infinitely pointy peaks, as well as "lepto" distributions with flat peaks. It's all about the tails. See