I need to compute the absolute moment of a Laplacian distribution. I just see in wikipedia that
If X ~ Laplace(0, b) then |X| ~ Exponential(b ^ −1)
where for exponential distribution
E[X^n]=(n!)/(lambda ^ n)
Therefore, the absolute moment of a laplacian is estimated as follows
E[|X^n|]=-(n!)/(b ^ n)
I would like to know is there any general formula for computation of absolute moment of a Laplacian distribution?
Yes, you can find it by using its formula given by its definition. However, the following steps are useful.
1. Define the absolute moment for Laplace distribution in mathematical form,
2. Split the integral from minus infinity to plus infinity as the sum of two integrals; one from minus infinity to zero and other from zero to plus infinity by defining the absolute function.
3. Use of gamma functions will evaluate both the integrals.
The procedure is quite similar to the one used for the normal distribution.
Please see the formula in the attachment. However, I can send you the scan copy of the calculation within a couple of days if needed.
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