ok i'm not bumping this thread, just saying that i have now got to the point where i need to express
(1/µ) - (1/2y) - y/(2*(µ^2))
in the form
yθ + b(θ)
Appreciate any help
Can anyone tell me how to prove the Inverse Gaussian distribution belongs to the exponential family? I've shown it with both the Poisson and the exponential distribution itself, but am struggling with the Inverse Gaussian being more complicated.
For anyone that doesn't know, it takes the form:
f(y)=(sqrt(2*pi*ф*(y^3)))*exp(-((y-µ)^2)/(2*pi*(µ^2)*y)) where y,ф,µ >0