#### fullofquestions

##### New Member

Page 31 bottom, it reads:

"Kurtosis greater than three (>3), which is the same thing as saying “excess kurtosis > 0,” indicates

**high peaks and fat tails (leptokurtic)**. Kurtosis less than three (<3), which is the same thing as saying “excess kurtosis < 0,” indicates lower peaks.

Financial asset returns are typically considered leptokurtic (i.e., heavy or fat-tailed)"

Page 32 top, it reads:

"For example, the logistic distribution exhibits leptokurtosis (heavy-tails; kurtosis > 3.0):

GRAPH

A probability distribution with “thicker tails” or “heavier tails” than the normal distribution has kurtosis > 3 and it called leptokurtic.

When a distribution is less peaked than the normal distribution, it is said to be platykurtic. This distribution is characterized by less probability in the tails than the normal distribution. It will have a kurtosis that is less than 3 or, equivalently, an excess kurtosis that is negative."

In the GRAPH listed we have the standard normal distribution in blue. Then we have a platykurtic distribution, one with lower peak, in purple. The platykurtic distribution CLEARLY has more probability(or samples rather) in the tails than the normal distribution. Can someone please explain the following:

1. what is a fat tail? Is it a tail with more *meat* on it, i.e. more height per unit area, much like a platykurtic distribution or is it somehow how much farther the tail extends ouT from the mean? In my opinion:

a. Leptokurtic distribution clearly has highest peak but quickly contours very close to the X axis. Therefore I see it as a 'thin' tail

b. Mesokurtic distribution, i.e. standard distribution, has a medium sized peak and the tails, in either direction contour closer to the X axis slower than the leptokurtic example. In this case there are more probabilities in the tails than in the leptokurtic case.

c. Platykurtic distribution, has the lowest peak and the tails contour to the X axis way more gradually and therefore has more probabilities in the tails. The tails are taller than compared to the leptokurtic and mesokurtic distribution.

2. is a fat tail any different from a heavy tail?

Please advise and correct where I've mistaken. Thank you.