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Calculate the first 4 Moments - Generalised Error Distribution?

Posted 8 years ago

Dear Community,
rt ? D(?) and its a GED. Density is given as:

$fGED (x; \mu, \sigma, \nu) =$ $\frac{1} {2\sigma \nu ^{1/\nu }2 \Gamma \left(\frac{1}{\nu }+1\right)}$ $e^{(-\frac{1}{\nu}\frac{ | x-\mu |^\nu }{\sigma ^{\nu} })}$

Given that $\mu = 0$

They gave me the Tip that: $\frac{ \Gamma (\frac{a+1} c) } {{cb^{ \frac{a+1}{c} }}}$ $=\int_0^{\infty } x^a e^{-\text{bx}^c} \, dx$

Is their a way to calculate the first 4 Moments in Mathematica? I didn't find a Method in the Forum or in Google :)

Cheers

Meister Yoda

POSTED BY: Meister Yoda
2 Replies

Perhaps use:

a = ProbabilityDistribution[ ......]

and the using CentralMoment:

CentralMoment[a,1]
CentralMoment[a,2]
CentralMoment[a,3]
CentralMoment[a,4]
POSTED BY: Sander Huisman

Also have a look at:

ExponentialPowerDistribution
POSTED BY: Sander Huisman
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