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?
