Actuarial Outpost Equilibrium Distribution and LER
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#1
10-28-2009, 08:41 PM
 badmaj5 Member CAS Join Date: Sep 2005 Location: Chicago, IL Posts: 454
Equilibrium Distribution and LER

The formula for the CDF of the equilibrium distribution would work out to be the same as the LER, correct? I could see that coming in handy if we were given some made up density and asked to compute the LER.
#2
10-28-2009, 09:18 PM
 volva yet Note Contributor Join Date: Feb 2006 Location: Nomadic Studying for GHC/DMAC College: PSU '07 Favorite beer: Oskar Blues Old Chub Scotch Ale Posts: 4,948

Quote:
 Originally Posted by badmaj5 The formula for the CDF of the equilibrium distribution would work out to be the same as the LER, correct? I could see that coming in handy if we were given some made up density and asked to compute the LER.
Isn't the LER always the following?

$\frac{E[X ^d]}{E[X]}$
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#3
10-28-2009, 09:26 PM
 badmaj5 Member CAS Join Date: Sep 2005 Location: Chicago, IL Posts: 454

LER(d) = E[X /\ d]/E[X].
Equilibrium Dist = [integral from 0 to d of S(X)]/E[X]
#4
10-29-2009, 12:52 AM
 chicken_po_boy Member CAS Join Date: Nov 2008 Location: 401 Poydras New Orleans, LA 70130 Studying for Nothing Ever Again College: been there, done that Favorite beer: You gonna finish that? Posts: 2,090

Is the term "equalibrium distribution" used in Loss Models? I'm using ASM and I don't remember it being referred to by that name.
#5
10-29-2009, 01:04 AM
 Clam Chowdah Member CAS Join Date: Aug 2008 Location: Derry, ME Studying for CAS 5 Favorite beer: Pick Pole Pale Ale Posts: 1,408

I wouldn't worry about that one. Is it on the SOA 289?
#6
10-29-2009, 07:10 AM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 7,220

Quote:
 Originally Posted by chicken_po_boy Is the term "equalibrium distribution" used in Loss Models? I'm using ASM and I don't remember it being referred to by that name.
It's in both. But yes, not too important.
#7
10-29-2009, 10:06 AM
 volva yet Note Contributor Join Date: Feb 2006 Location: Nomadic Studying for GHC/DMAC College: PSU '07 Favorite beer: Oskar Blues Old Chub Scotch Ale Posts: 4,948

Quote:
 Originally Posted by badmaj5 LER(d) = E[X /\ d]/E[X]. Equilibrium Dist = [integral from 0 to d of S(X)]/E[X]
Equilibrium Dist = LER? Hmm!
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How to explain actuarial exams to someone else...

Good Einstein quote - "One had to cram all this stuff into one's mind for the examinations, whether one liked it or not. This coercion had such a deterring effect on me that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year."
#8
10-29-2009, 11:20 AM
 badmaj5 Member CAS Join Date: Sep 2005 Location: Chicago, IL Posts: 454

I really don't see any reason why that SHOULDN'T be the case...
#9
03-15-2019, 04:04 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 113

just by looking at a Lee diagram, I can see they are not the same thing... LER is the ratio of 2 areas, fe is the ratio of a segment to the total area, and it's a proper distribution that adds up to 1....
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