Let Y1, Y2,..., Yn denote a random sample from a Poisson-distributed population with

Chapter 16, Problem 16.11

(choose chapter or problem)

Let Y1, Y2,..., Yn denote a random sample from a Poisson-distributed population with mean . In this case, U = Yi is a sufficient statistic for , and U has a Poisson distribution with mean n. Use the conjugate gamma (, ) prior for to do the following. a Show that the joint likelihood of U, is L(u, ) = nu u!() u+1 exp + n + 1 . b Show that the marginal mass function of U is m(u) = nu(u + ) u!() n + 1 u+ . c Show that the posterior density for | u is a gamma density with parameters = u + and = /(n + 1). d Show that the Bayes estimator for is B = Yi + n + 1 . e Show that the Bayes estimator in part (d) can be written as a weighted average of Y and the prior mean for . f Show that the Bayes estimator in part (d) is a biased but consistent estimator for .

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back