# No Skewness but Excess Kurtosis

Hi, Is it possible to have “No Skewness but Excess Kurtosis”

Yes. It just means flat peak, fat tails, but symmetric.

^ Wrong. Leptokurtic (Excess kurtosis): MORE peaked, fat tails There is an excellent picture on the top of page 303 in the CFAI books. It shows a distribution that has skewness of zero, but has excess kurtosis.

thank you!

platykurtic curve has thinner tails than normal distribution curve. Is that correct?

The difference between T-distribution and Platykurtic is that T-distribution has fatter tail compared to normal distribution whereas Platykurtic has thinner tail compared to normal distribution The similarity between T-distribution and Platykurtic is that both are less peaked compared to normal distribution.

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I think that the point saminathan made needs to be stressed. In the book CAFI v1 p330, Kurtosis is crearly explained as the peakedness of the distribution. The normal distribution has a kurtosis of 3 (and this is the same as saying 0 excess kurtosis). Leptokurtic - kurtosis > 3 (excess kurtosis > 0) Mesokurtic - kurtosis = 0 Platykurtic - kurtosis < 3 (excess kurtosis < 0) It seems that in many resources all over, leptokurtic is synonimous to: 1. more peaked than normal distribution 2. fatter tails than normal distribution Please note that the t-distribution, for a degree of freedom =1 it is: 1. less peaked than normal distribution 2. fatter tails than normal distribution When the degrees of freedom increase to infinity 1. just as peaked as the normal distribution 2. fat tails just as fat as normal distribution fyi

saminathan Wrote: ------------------------------------------------------- > The difference between T-distribution and > Platykurtic is that T-distribution has fatter > tail compared to normal distribution whereas > Platykurtic has thinner tail compared to normal > distribution > > The similarity between T-distribution and > Platykurtic is that both are less peaked > compared to normal distribution. Platykurtic is an adjective that can describe oodles of distributions and a T-distribution is a well-defined distribution that you get by dividing a normal r.v. by a the square root of a chi-square r.v… This is like saying the difference between a Ferrari and slow is that a Ferrari is that a Ferrari is only slow when its wheels fall off.

And having been a professional statistician for 20 years or more, I have never heard another statistician use the words platykurtic, etc. except when some text book forces them to.