Calculate the first 4 Moments - Generalised Error Distribution?

Questions
1

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 :slight_smile:

Cheers

Meister Yoda

2

Perhaps use:

a = ProbabilityDistribution[ ......]

and the using CentralMoment:

CentralMoment[a,1]
CentralMoment[a,2]
CentralMoment[a,3]
CentralMoment[a,4]
3

Also have a look at:

ExponentialPowerDistribution