Talk:Excess kurtosis

Reader feedback: Leptokurtic distribution con...
70.43.171.150 posted this comment on 13 February 2016 (view all feedback).

"Leptokurtic distribution contains fat tails. Thus, while many returns may cluster, there are also more 'extreme' observations. Thus the suggestion to structure a portfolio as leptokurtic is not correct."

Any thoughts?

LadyGeek 15:51, 13 February 2016 (EST)

Blbarnitz has updated the page. --LadyGeek 17:36, 14 February 2016 (EST)

Reader feedback - content is incorrect
You pictures of distributions related to kurtosis make no sense. Kurtosis has nothing to do with the height of the peak of the distribution.

The peaks tell you nothing about the tails; they are unrelated. You can have an infinite peak and thin tails, and you can have an infinite peak and fat tails. You can have a flat peak and thin tails, and you can have a flat peak and fat tails. Kurtosis measures outliers only.

The description of kurtosis as measuring "flatness," or anything at all about the peak, is outdated and simply wrong. You can have an infinitely pointy peak with negative excess kurtosis, and you can have a flat peak with near infinite kurtosis. A great way to understand this from a finance point of view is this: take a distribution with any shape peak you want. Then mix it with it a very outlier-prone distribution, with small mixing probability. In finance terms, this mixing distribution represents the "Black Swan," or the occasional very rare event where the data are abnormal. The resulting mixed distribution will have huge kurtosis, but the shape of the peak will not change because the mixing probability is small. For negative kurtosis with infinite peak, consider a bounded distribution, eg beta(1,.5). Having more in the peak does not "lead to tails" as erroneously stated. See www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753

Your descriptions about the peak, as it relates to kurtosis, are completely wrong. Please have a look at the Wikipedia page. Kurtosis tells you nothing about the shape of the peak, flat, pointy, etc.
 * The referenced article: Kurtosis as Peakedness, 1905 – 2014. R.I.P.
 * Wikipedia: Kurtosis - Wikipedia
 * NASDAQ: Excess kurtosis Definition - NASDAQ.com - An authoritative investing source.
 * Kurtosis Excess -- from Wolfram MathWorld - explains the discrepancy in the definitions.
 * 1.3.5.11. Measures of Skewness and Kurtosis, from the National Institute of Standards and Technology (NIST) - which also notes a discrepancy.

I don't have the experience to revise this page. Can an expert please assist? --LadyGeek 15:03, 25 March 2018 (UTC)