How derive a CDF from MGF directly ?

[nikozm]

Hi,

i am trying to develop a CDF from a given MGF. The standard way of using the inverse Laplace transform etc.. is not feasible due to complexity of MGF.

I was woldering if there is another straighforward direction via integration or differentiation method to produce the CDF (or PDF) directly from MGF ?

Any help will be useful

Thank you in advance

 

[mathman]

Hi,

i am trying to develop a CDF from a given MGF. The standard way of using the inverse Laplace transform etc.. is not feasible due to complexity of MGF.

I was woldering if there is another straighforward direction via integration or differentiation method to produce the CDF (or PDF) directly from MGF ?

Any help will be useful

Thank you in advance

No. You need the inverse Laplace transform. In passing when I was introduced to this material, we used Fourier transform to get characteristic function (the moments are available here too). The main advantage is that to get PDF you just needed the inverse Fourier transform, which looked just like the Fourier transform (sign change in exponential).