C3 - De Moivre's Law

The force of mortality for De Moivre's Law is defined as u(x)=1/(w-x) on page 78 of Act. Math. and page 17 of the Arch manual. Then it is defined as ux(t)=1/(w-x-t) on page 38 of the Arch manual. I don't understand the difference between these two formulas. Why is the force of mortality sometimes a function of t and sometime not under De Moivre's Law? Which do you use when?
Thanks in advance for your help.

[Gandalf]

The force of mortality for De Moivre's Law is defined as u(x)=1/(w-x) on page 78 of Act. Math. and page 17 of the Arch manual. Then it is defined as ux(t)=1/(w-x-t) on page 38 of the Arch manual. I don't understand the difference between these two formulas. Why is the force of mortality sometimes a function of t and sometime not under De Moivre's Law? Which do you use when?
Thanks in advance for your help.
It depends on what "x" means. In the context of Arch, x is age at issue so x+t is current age when mu is being evaluated. On page 78 of Act Math, x is the current age when mu is being evaluated. So the formulas are the same.

Thanks. I knew it would end up being something simple like that.

[Bullseye]

2 things :

1) De Moivres Law is very very easy (see below)

2) You will NEVER NEVER pass Exam 3 if you are just trying to remember blind formulas. You need to understand them What do they mean? How do I apply them in various situations? It takes a lot of studying to achieve this level of understanding, but it is necessary.

De Moivres law just assumes people die in a linear fashion. If there is 100 people alive at time zero and they can live a maximum of 50 years (w = 50) then 2 people will die each year:
at time zero: 100 people are alive and the probability of any one of them dying at that moment is 1/50 = u(x) (they can die with equal probability any time in the next 50 years)

at time 20: the amount of people alive are 60 (2 people die each year) and the probability of them dying at that moment is 1/30 = u(x) There are thirty years left to live and they can die with equal probability at any time in those thirty years.

Thus if the simple question was what is the probability of someone at time zero living to at least age 20. The answer is 60 people alive at age 20 / 100 people originally alive = 60%.

What is the probability of someone who is 10 living to at least 20 ? = 60 people alive at age 20 / 80 people alive at age 10 = 60/80 = 75%

It makes sense that the number is higher because the person has already survived the first 10 years.

Hope this helped.

Thanks Bullseye, I needed that.

Would it be accurate to say that De Moivre's Law assumes linear interpolation (i.e. UDD), since tPx is linear when you hold x constant and vary t, but is not linear when you hold t constant and vary x (i.e. tPx is linear within years but not between years)?

[Toonces]

Not exactly sure what you are trying to say, but "linear interpolation" is essentially De Moivre's law only applied to within a year. So, using De Moivre's law by default must mean you are using UDD within years.

[J-Man]

Careful. DeMoivre's Law is a special case of UDD. UDD is linear interpolation between whole years of age. It says nothing about the number of people alive at those whole years of age (this might not be linear).

[GuoQiang]

Then, how about Constant Force?