Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Exam 4/C - Construction and Evaluation of Actuarial Models
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Salary Surveys
Property & Casualty, Life, Health & Pension

Health Actuary Jobs
Insurance & Consulting jobs for Students, Associates & Fellows

Actuarial Recruitment
Visit DW Simpson's website for more info.
www.dwsimpson.com/about

Casualty Jobs
Property & Casualty jobs for Students, Associates & Fellows


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 05-22-2018, 11:42 AM
RockOn RockOn is offline
Member
SOA
 
Join Date: Dec 2013
Studying for Exam C
Favorite beer: Polygamy Porter
Posts: 53
Default SOA #131

Hello!

I think I understand this problem for the most part. Just need a little help in understanding how the following formula was derived (in SOA solution):

(-1/lambda)*ln(1-u)

Is this supposed to be the inverse of the poisson pgf?

Thank you!
__________________
EXAMS: P | FM | MFE | MLC | C | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
Reply With Quote
  #2  
Old 05-22-2018, 11:57 AM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,617
Default

Quote:
Originally Posted by RockOn View Post
Hello!

I think I understand this problem for the most part. Just need a little help in understanding how the following formula was derived (in SOA solution):

(-1/lambda)*ln(1-u)

Is this supposed to be the inverse of the poisson pgf?

Thank you!
No. When frequency of events is Poisson with mean lambda, the "times" (or fractions of an exposure unit) between events are mutually independent Exponential random variables with mean theta = 1 / lambda. Also, given a value U of a Uniform random variable on (0,1), the inversion-simulated value of an Exponential is - theta ln ( 1 - U ).

Technically, #131 asks about a Poisson _Process_, and Poisson Processes are no longer on the syllabus. However, it could have just said that you were simulating a Poisson random variable and then it would be on the syllabus.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
Reply With Quote
  #3  
Old 05-22-2018, 11:57 AM
RockOn RockOn is offline
Member
SOA
 
Join Date: Dec 2013
Studying for Exam C
Favorite beer: Polygamy Porter
Posts: 53
Default

Quote:
Originally Posted by RockOn View Post
Hello!

I think I understand this problem for the most part. Just need a little help in understanding how the following formula was derived (in SOA solution):

(-1/lambda)*ln(1-u)

Is this supposed to be the inverse of the poisson pgf?

Thank you!
...I meant to say: Is this supposed to be the inverse of the poisson CDF?
__________________
EXAMS: P | FM | MFE | MLC | C | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
Reply With Quote
  #4  
Old 05-22-2018, 12:00 PM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,617
Default

Quote:
Originally Posted by RockOn View Post
...I meant to say: Is this supposed to be the inverse of the poisson CDF?
Again, no. See my answer to your first post on #131.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
Reply With Quote
  #5  
Old 05-22-2018, 12:53 PM
RockOn RockOn is offline
Member
SOA
 
Join Date: Dec 2013
Studying for Exam C
Favorite beer: Polygamy Porter
Posts: 53
Default

Quote:
Originally Posted by Jim Daniel View Post
Again, no. See my answer to your first post on #131.
Thank you! I hadn't seen your first post when I posted my second post.

Thank you again!
__________________
EXAMS: P | FM | MFE | MLC | C | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 07:55 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.31605 seconds with 9 queries