The thing about tails becoming, however, should, about

LiquidAssets10

t to Z to leptokurtic

As N gets larger, t approaches Z i.e. becoming more peaked and thinner tail.
A Leptokurtic is more peaked than Z, however, it has fatter tail than Z?

I thought as a distribution gets more and more peaked, its tail should get thinner and thinner?

marsilni

revenant Wrote:
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> t to Z to leptokurtic
>
> As N gets larger, t approaches Z i.e. becoming
> more peaked and thinner tail.
> A Leptokurtic is more peaked than Z, however, it
> has fatter tail than Z?
>
> I thought as a distribution gets more and more
> peaked, its tail should get thinner and thinner?

Not necessarily. Fat tails (kurtosis) have nothing to do with peaks. T distribution has lower peaks than normal, however leptokurtic distribution (as you said) have higher peaks. Distribution density shows distribution of probability of 1 across outcomes. If distribution has fat tails, it has more weight in the tails. In case of T-distribution weight is borrowed from the central part relatively uniformly, whereas leptokurtic distributions shift more weight to the center (high peak) and tails (fat tails) and borrow weight from everywhere else. Of course, t-distribution is not leptokurtic.

Micholien

maratikus Wrote:
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>
> Not necessarily. Fat tails (kurtosis) have nothing
> to do with peaks. T distribution has lower peaks
> than normal, however leptokurtic distribution (as
> you said) have higher peaks. Distribution density
> shows distribution of probability of 1 across
> outcomes. If distribution has fat tails, it has
> more weight in the tails. In case of
> T-distribution weight is borrowed from the central
> part relatively uniformly, whereas leptokurtic
> distributions shift more weight to the center
> (high peak) and tails (fat tails) and borrow
> weight from everywhere else. Of course,
> t-distribution is not leptokurtic.


Good explaination.

orang3eph

Z has thinner tail compare to both; hence Z has smaller number of large deviations from mean.

t with small n has lesser number of small deviations from mean whereas lepto has larger number of small deviations from mean.

Is that all we need to know?

Thanks.