T distribution

[pd_sn]

Hi David,

T distribution is less peaked than Normal Distribution. Then how do we explain that it has kurtosis greater than 3? This thing is really confusing. Also, can heavy tails be part of both Leptokurtic and platykurtic distributions ?

 

[ShaktiRathore]

please refer to the link:
http://forum.bionicturtle.com/threads/kurtosis-and-peakedness.4758/

thanks

 

[David Harper CFA FRM]

Thanks Shakti! Per that earlier thread, the student's does have a higher peak if you compare both with the same variance (I learned that in Carol Alexander's excellent MRA vol I, btw). Heavy tails are leptokurtic only; I think this is the most reliable definition of heavy tails: kurtosis > 3.0 (normal) = leptokurtic/leptokurtotic. What i mean is that textual adjectives (tall/peaked/heavy/light) appear to leave some interpretive wiggle room, but the heavy tails has a specific, concrete mathematical definition that is not susceptible to the optical illusion created by the typical student's t plot.