FRM - 1 : Kurtosis and Curve Shape for Leptokurtic , Mesokur

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FRM - 1 : Kurtosis and Curve Shape for Leptokurtic , Mesokur

Postby ashok.kothavle » Mon Jul 21, 2014 9:56 am

Yesterday during the lecture we were informed that Leptokurtic has peak higher than the Mesokurtic (i.e. Normal distribution) curve and has fat tails while Platykurtic curve has peak smaller than Normal curve and has thinner tail.

However, in the question bank (Schweser Notes - Quantitative Analysis - Distributions.pdf - Question 3 - #38344), it is mentioned that as compared to Normal distribution, the t - distribution is LESS PEAKED with more area under the tails. This means that (1) t - distribution is Platykurtic and is also a fat tailed since it has more area under the tails. So my understanding is even the PLATYKURTIC distributions can also be FAT TAILED.

Kindly guide if my understanding is correct or I am missing something? If my understanding is correct, then I guess the CURVE graph as shown in the material

- PAGE No 47, may need a re look and might need correct depiction as it may lead to wrong interpretation.


Ashok D Kothavle

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FRM - 1 : Kurtosis and Curve Shape for Leptokurtic , Mesokur

Postby edupristine » Tue Jul 22, 2014 7:05 am

Hi Ashok,
Please be noted that student’s t- distribution is leptokurtic and not platykurtic.
If you try your hands in google, what you will come across is that Leptokurtosis is about peakedness (which means higher peaks and fatter tails). But, this does not hold true in every circumstance.
A standard example is that of a t- distribution which is less peaked than normal, but it is always leptokutic (kurtosis>3).
The visual shape of a distribution should not be the only criteria to define a distribution else it would lead to confusing results.
What heavy tail in student’s t- distribution (leptokurtosis) means is that :
CDF of t- distribution (at very low or very high x%) < CDF of normal distribution (at the same x %)
(CDF: Cumulative Distribution Function)
A leptokurtic distribution implies more area in the tails as compared to normal.
So just to summarize:
1) Never judge a distribution to be plato, lepto or meso just by observing the peaks. This is not a thumb rule to classify a distribution although in some texts you will find this definition in a very prominent manner. However, this does not always hold true as explained above in case of t- distribution.
2) You need to understand the logic behind classifications of distributions. In case of t distribution, it is appropriately called leptokurtic because of heavier tails as compared to normal (reasoning of heavy tails already described above from a risk point of view).
3) So, effectively if you ever want to know in which category the distribution will fall in, always look for heavy tails or thinner tails (or simply tail density) as the criterion. The peakedness criterion might show contrasting results at times. Do not rely on peakedness.
Hope it was helpul. Nevertheless please feel free to discuss again. I will be happy to take this further.

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Postby ashok.kothavle » Tue Jul 22, 2014 8:23 am

Thanks a lot for the really good explanation. This graphical representation has always confused me since long, and finally got good answer today. Henceforth, I will check the Kurtosis value than relying on graph. Thanks again.

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