Thread: Inverse Gaussian Exponential Family

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

Many thanks,
Shaun

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

Shaun

Originally Posted by Shaun Gill

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

Many thanks,
Shaun

Have you read this and this.

I have and I'm still stuck. Can you point me in the right direction ?