test for given survival functions

[Sox34]

So, if a function is given and we're asked to see if it can serve as a force of mortality, the tests are
1. must always be positive, (although not necessarily increasing which was key for last fall's CAS exam)
2. the integral from 0 to infinity of the function must equal infinity

What are the corresponding tests if a function is given and we need to test if it can serve as a survival function?
1. must be [0,1]
some of the other things I've thought of do not work for certain mortality laws.
Anyone know the general rules?

[Sox34]

I think I have written down somewhere that s(x) has to be increasing although I do not know if that makes sense to me...

[wat?]

Originally Posted by Sox34

I think I have written down somewhere that s(x) has to be increasing although I do not know if that makes sense to me...

• s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]
• s(0) = 1
• lim (x-->inf) s(x) = 0
• s(x) is right-continuous

[Sox34]

Originally Posted by wat?

[list][*]s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]

yeah i must have had a brainfart when i wrote that down. thanks.

[TwinsFan1987]

Originally Posted by wat?

• s(x) must be non-increasing. [You can't have a better chance of survival as you get older. (Well, not theoretically - there is the anomaly of newborns.)]

Actually, the condition doesn't mean that you have a lesser chance of dying as you get older. Many real-life mortality tables account for the high infant mortality rate but still have decreasing survival functions.

What the decreasing (actually non-increasing) survival function means is that no one can be added to the pool - once you die, you're out. If the survival function is level over a time period, then that means that no one dies during that period.

I hope that this helps.

[wat?]

Originally Posted by TwinsFan1987

Actually, the condition doesn't mean that you have a lesser chance of dying as you get older. Many real-life mortality tables account for the high infant mortality rate but still have decreasing survival functions.

What the decreasing (actually non-increasing) survival function means is that no one can be added to the pool - once you die, you're out. If the survival function is level over a time period, then that means that no one dies during that period.

I hope that this helps.

Thanks. My mistake that I didn't check it too carefully - was on my way out of the office.