Actuarial Outpost Survival Function Inferences
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#1
11-10-2018, 12:30 PM
 JohnTravolski Member Non-Actuary Join Date: Aug 2016 Posts: 48
Survival Function Inferences

Observe the following problem:

I know that the survival function is clearly a decreasing function of x and t, and an increasing function of gamma, but I'm not sure what else they could possibly want?

Am I missing something here? How would you answer the question?

This is from "Actuarial Mathematics and Life-Table Statistics" by Eric V. Slud by the way.
#2
11-10-2018, 05:24 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,711

Quote:
 Originally Posted by JohnTravolski Observe the following problem: I know that the survival function is clearly a decreasing function of x and t, and an increasing function of gamma, but I'm not sure what else they could possibly want? Am I missing something here? How would you answer the question? This is from "Actuarial Mathematics and Life-Table Statistics" by Eric V. Slud by the way.
You can deduce that S(n)=(gamma)^{n^2}, more generally that, for a fraction f, S(n+f)=(gamma)^{n^2+2nf}S(f), which determines all values of S if you were given the values of S(f) for 0 < f< 1. To get this just write
S(n+f) = 1p{n-1+f} 1p{n-2+f} ... 1pf fp0 and use the formula for 1px.
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#3
11-10-2018, 07:52 PM
 JohnTravolski Member Non-Actuary Join Date: Aug 2016 Posts: 48

You're right, I see it now. Thank you.