Finding the scale parameter ch13

[Molly]

Hi all,

This might be something super simple that im missing, but im struggling to know which one to pick out as the scale parameter \phi.

i can find the natural parameter \theta being the coefficient of Y in the exponential family form. This means i can find b(\theta) easily by being the other term in the numerator.

Im struggling to decide which term will be \phi. For example i just did chapter 13 Q6 and the denominator is 1/n, i wanted to chose \phi to be 1/n because of this, but the answer was n. Please could someone explain how to deduce \phi and therefore a(\phi)?

Thanks!

 

[Andrea Goude]

Hi Molly

a(phi) is a function of phi, you work out a(phi) first, then work out phi, so in Q6 the function is 1/n, and phi is n.

In CS1 this is the parameterisation we use for the Binomial distribution.

Another approach is to take the scale parameter as the other parameter, so in Q6 phi is n, as theta is mu.

Thanks Andrea

 

[Molly]

Hi Molly

a(phi) is a function of phi, you work out a(phi) first, then work out phi, so in Q6 the function is 1/n, and phi is n.

In CS1 this is the parameterisation we use for the Binomial distribution.

Another approach is to take the scale parameter as the other parameter, so in Q6 phi is n, as theta is mu.

Thanks Andrea

ah that second approach you mentioned makes much more sense in my head, i will use that,
thank you!