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

2 comments:

  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 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753/pdf/nihms-599845.pdf

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