Find moment generating function

Question

I want to find the moment generating function $M(t)$ for distribution

$$ f(x) =e^{-(ax)^{2}}*(1-e^{-(ax)^{2}})^{b-1}*[-log(1-e^{-(ax)^{2}})]^{r-1} $$

$$ M(t):=E(tX) = \int_0^\infty e^{tx}*f(x)dx \,. $$ But I have a problem.

not $\int_{0}^{+\infty}e^{tx}f(x)dx?$ – math110 Mar 09 '15 at 10:51 — math110, Mar 09 '15 at 10:51
thanks my friend i correct the quastion – Mundher Mar 10 '15 at 06:42 — Mundher, Mar 10 '15 at 06:42

score 0 · Answer 1 · answered Dec 14 '15 at 09:12

0

The moment generating function is simply the Laplace transform. Since the Laplace transform of a convolution is the product of Laplace transform you simply have to compute the Laplace transform of each term and then multiply them.

answered Dec 14 '15 at 09:12

user47354

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Find moment generating function

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