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March 17th, 2017, 03:44 AM   #1
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inverse gaussian distribution

hi,

for X~IG(m,l), IG:inverse gaussian, the characteristic function
C_X(t)=E[exp(itX)]=exp{m/l (1-(1-2im^2 t/l)^1/2)}

i need help to demonstrate that:
and differentiating C_X(t) by r times and letting t=0

E[X^r]=m^r \sum_{k=0}^{r-1}(r-1+k)!/(k!(r-1-k)!)(m/2l)^k
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March 21st, 2017, 10:18 PM   #2
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Anyone has this book

Hi,
Anyone has this book:
"Monograph on inverse gaussian distribution" by WASAN Mandanlal T. (1966)?
It's very helpfull for me.
Thanks
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