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SP9 M16 pg13 error in Leptokurtic graph

J

Johann

Member
Hi All,
Just a quick question, I think the solution to the question on pg16 of Module 16 is showing the wrong distribution to be Leptokurtic (i.e. it is showing the t-distn with gamma = 1) from my understanding this should be platykurtic compared to the standard normal distribution. Is this correct or am i missing something?

Thanks
Johann
 
Hello Johann

Just had a quick look at Sweeting P157/158 and think the graph is OK. When gamma = 1 we have the Cauchy distribution, which is renowned for its fat tails (leptokurtic).

I also tried a sense check with the PDF on P157 of Sweeting, putting in gamma = 1. I get:

f(x) = (1/β pi) {1 + [(x-α)/β]^2}^-1

This looks like it has power decay (heavier tails) whereas the normal distribution has exponential decay (lighter tails).

Is this OK?
Anna
 
Okay thank you for this Anna, so just to confirm (heavier tails/leptokurtic) distributions produces more extreme events than the (lighter tails/platykurtic) distributions? Think I may have been missing this point?
 
Hi Johann, yes, leptokurtic distributions typically have a fatter tailed / thinner peaked PDF than a normal distribution would have. This means that it assigns higher probabilities to extreme events.
 
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