Sponsored Ads
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 Associates
Actuarial Openings: Life, P&C, Health, Pensions, Finance
Actuarial Careers, Inc. ®
Actuarial Jobs Worldwide
Search positions: Geographic Region, Specialization, Salary

Results 1 to 1 of 1

Thread: Linear Exponential Family & Inverse Exponeital Distribution

  1. #1
    Actuary.com - Level II Poster
    Join Date
    Oct 2008
    Posts
    75

    Arrow 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!
    Last edited by 777888; April 20th 2012 at 04:06 AM.

Thread Information

Users Browsing this Thread

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

Similar Threads

  1. Method of distribution functions and Exponential random variables questions
    By zzod in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 5
    Last Post: August 10th 2010, 08:23 PM
  2. Exponential distribution with deductible and limit
    By edt966 in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 3
    Last Post: January 11th 2009, 03:08 AM
  3. Exponential Distribution question
    By Eunye in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 2
    Last Post: April 24th 2008, 09:39 PM
  4. Exponential distribution
    By Anu Dhanuka in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 5
    Last Post: November 15th 2007, 11:53 AM
  5. Exponential Distribution
    By Hobogov in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 4
    Last Post: February 2nd 2007, 05:09 PM

Bookmarks - Share

Bookmarks - Share

Posting Permissions

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