Inverse Fourier Transform help (pdf from first characteristic function)

2012 5 15
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Hello,
I have a program that generates a truncated version of the second characteristic function (cumulant generating function) of a random variable. From this I calculate first characteristic function (moment generating function), using the following loop:
syms s x
firstchar = 1;
for i = 1:k
firstchar = firstchar*exp(s^(i)*cumulant(i)/factorial(i));
end
Next I take the inverse Fourier Transform of the first characteristic function to get the pdf. This is all done symbolically with the following code
f_cs = simplify(eval(firstchar));
f_cs = subs(f_cs, s, -1i*x);
pdf = ifourier(f_cs, x, t);
In most cases (for i > 2 in the above loop) I am not able to find a closed form of the pdf.
Can anyone help? I don't necessarily need to do this symbolically, and have tried using ifft, but nothing seems to work. Any ideas?
Thank you.

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Salvatore
Salvatore
2012-5-15

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