With kurtosis defined as:kurtosis = E[ (X - Xbar)^4 ] / (sigma^4) - 3(so normal distribution will have kurtosis=0), would we expect kurtosis to be +ve or -ve for a fat-tailed distribution (i.e. fat tailed as compared to the normal distribution), e.g. t-distribution?I normally would've said - "higher" since the 4-th power in the numerator would be larger for larger deviations from the mean than the denominator.But mathworld says: "A distribution with a high peak [and kurtosis>0] is called leptokurtic, a flat-topped curve [and kurtosis<0] is called platykurtic, and the normal distribution is called mesokurtic. "Which is correct? Thanks...Mathworld Kurtosis

fat tails = leptokurtic

kurtosis is the "peakedness" of the pdf

I think of kurtosis like this. Imagine you have a cdf full of grape jam (or strawberry if you prefer). I.E., the area under the curve is full of some fluid substance. Suppose you pinch it with one finger some distance below the mean and the other finger some distance above. Some jam would go up into the center of the CDF, and some would ooze out into the tails. Thus, the tails would be fatter than a normal cdf, and the center would be more peaked. With positive excess kurtosis (kurtosis higher than the normal distribution), the probability of being moderately far from the mean is decreased, the probability of being very close to the mean is increased, and the probability of be extremely far from the mean is increased.

Thanks - the jam analogy hits the spot :-)But we can get fat tails two ways then. We can "squeeze" the middle and thus end up with a peaked distribution and fat tails. Or we can flatten the top and push the distribution out to its tails - of course, this also increases variance and maybe that cancels it out, but I just tried excel to calculate the kurtosis of Uniform[-50,+50]. Uniform[-50,+50] has higher probability of extreme outcomes than Normal(0,1), but has lower kurtosis.

bskilton81 like the analogy!