D.W. Simpson Worldwide Actuarial Recruitment Life Health Pension Casualty US Asia Australia Europe Salary Apply Ezra Penland Actuarial Recruiters Top Actuary Jobs Salary Surveys Apply Bios Casualty Health Life Pension ACTEX Publications / MadRiver Books The Experts in Actuarial Education Serving students worldwide for over 40 years S.C. Inernational, Ltd. Recruiting Actuaries and Risk Prof. Since 1986 Actuarial Jobs     Surveys     For Employers Pauline Reimer, ASA, MAAA Pryor AssociatesActuarial Openings: Life, P&C, Health, Pensions, Finance Actuarial Careers, Inc. ® Actuarial Jobs WorldwideSearch positions: Geographic Region, Specialization, Salary

# Thread: Linear Exponential Family & Inverse Exponeital Distribution

1. ## Linear Exponential Family & Inverse Exponeital Distribution

Suppose the model distribution X|Λ=λ is inverse exponential
f(x|λ) = λ exp(-λ/x) / x^2
and the prior distirbution for Λ is gamma with parameters α and θ.
(note: this belongs to the case of "exact credibility", so that the Bayesian and Buhlmann premiums are the same.)
In particular, the model distribution is in the linear exponential family, i.e. f(x|λ) = p(x) exp[r(λ) x] / q(λ).
Determine p(x), r(λ), and q(λ).

=======================================

Can anyone please explain how to solve this problem? It seems like I'm missing something because I have no idea how to get the exp[r(λ) x] part in this problem. How can I make the x to appear at the top when it is actually at the bottom for the inverse exponential density?

Any help would be greatly appreciated!

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•