Hi,
When I was reading about kurtosis, to me intuitively, I thought leptokurtic means there’s less fat tails than the normal distribution since the distribution is taller than the normal. However the book contradicts this:
The situation of more-frequent extremely large surprises that we described is one of leptokurtosis.
(Institute 428)
Institute, CFA. 2016 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. CFA Institute, 07/2015. VitalBook file.
The citation provided is a guideline. Please check each citation for accuracy before use.
However google image search contradicts this:
https://www.google.com.au/search?q=leptokurtic+platykurtic&biw=2520&bih=1331&source=lnms&tbm=isch&sa=X&sqi=2&ved=0ahUKEwi40aGhmabSAhVKG5QKHc7lC8YQ_AUIBigB#imgrc=_
Now I’m confused.
A leptokurtic distribution has:
- More probability near the mean than a normal distribution, say in the range μ ± ½_σ_
- More probability in the tails (say, above μ + 3_σ_ and below μ − 3_σ_)
- Less probability in the midranges: between μ − 3_σ_ and μ − ½_σ_, and between μ + ½_σ_, and μ + 3_σ_
Looks like the graphs are correctly drawn out here:
http://www.epixanalytics.com/modelassist/AtRisk/Model_Assist.htm#Presentng_results/Statistical_descriptions_of_model_outputs/Kurtosis_(K).htm
^^^
Hmm that link doesn’t appear to work… I’m referring tot he 6th graph from here:
https://www.google.com.au/search?q=kurtosis+wikipedia&client=opera&hs=aXU&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjv9tOD8afSAhWSNpQKHa79AHoQ_AUICCgB&biw=2520&bih=1331#tbm=isch&q=kurtosis&*&imgrc=SIGOWo7LXGsVeM:
To me, yes leptokurtic is slightly fatter tails than the normal distribution, but just barely not sure why you would call this fat tailed, what strikes me about that diagram is the fat tails on the platykurtic distribution which is what my intuition suggested would be the case. But no mention of this in the text… not sure why.
After some more searching, I’ve come to the conclusion that there is a lot of misinformed diagrams of these things, wikipedia seems to be consistent with what the CFA curriculum states and what S2000magician also said.
https://en.wikipedia.org/wiki/Kurtosis
The other thing to consider is the fact that if you have fat tails you end up having more large values at the fat tails then you get large values when you plug them into the kurtosis formula (since the variance deviations are taken to the power of 4), so the only way for platykurtic distributions to be less than 3 is for them to have less fat tails.
Also discussed in this video:
https://www.youtube.com/watch?v=Pf7awGwzy4k&t=20s
In Greek lepto means thin, small. Plati means wide. Kirtoma means hump. (Note it is not koortosis but kirtosis)
Leptokirtic means thin hump, platikirtic means wide hump. It all makes sense now.
I will not say on what Croatian word “kurtosis” associates me but that’s all same thing finally. 