Kurtosis and t-distribution

[thesame2]

As we learned from Quantitative part of the CFA textbook –
(1) Kurtosis and excess kurtosis deal with whether or not a distribution is more or less “peaked” than a normal distribution. For example, leptokurtic is used to describe a distribution whose sample kurtosis is larger than 3 and excess kurtosis is larger than 0. We also learned that leptokurtic distribution is more peaked and it has “fatter tails”, while platykurtic distribution is less peaked and it has “thin tails”.
(2) Student’s t-distribution is less peaked than a normal distribution, at the same time, t-distribution has “fatter tails”.
In this way, it seems like that t-distribution is neither leptokurtic nor platykurtic. Does it mean that we cannot describe the kurtosis of “t-distribution”?

 

[S2000magician]

The kurtosis of a Student’s t-distribution with 5 degrees of freedom in 9.
The kurtosis of a Student’s t-distribution with 10 degrees of freedom is 4.
Those are the only ones I calculated.
Leptokurtic.

 

[thesame2]

S2000magician wrote:
The kurtosis of a Student’s t-distribution with 5 degrees of freedom in 9.
The kurtosis of a Student’s t-distribution with 10 degrees of freedom is 4.
Those are the only ones I calculated.
Leptokurtic.

Thank you. But still have questions…
Per the CFA textbooks - leptokurtic distribution is more peaked and it has “fatter tails”; student’s t-distribution is less peaked than a normal distribution and has “fatter tails”.
If generally speaking, t-distribution is Leptokurtic. How do you explain the conflicts, which is leptokurtic distribution is more peaked than normal distribution while t-distribution is less peaked? Or probably I should let this question go as CFA exams may not care about it…

 

[S2000magician]

When the CFA textbooks say that leptokurtic distributions are more peaked than the normal distribution, they’re making a general statement that (like many, maybe most, general statements) isn’t universally true.
Your last sentence sums it up: it won’t appear on the exams.

 

[thesame2]

S2000magician wrote:
When the CFA textbooks say that leptokurtic distributions are more peaked than the normal distribution, they’re making a general statement that (like many, maybe most, general statements) isn’t universally true.
Your last sentence sums it up: it won’t appear on the exams.

okay. Thank you S2000magician!

 

[S2000magician]

thesame2 wrote:

S2000magician wrote:When the CFA textbooks say that leptokurtic distributions are more peaked than the normal distribution, they’re making a general statement that (like many, maybe most, general statements) isn’t universally true.
Your last sentence sums it up: it won’t appear on the exams.

okay. Thank you S2000magician!

My pleasure.