I should probably make the answer I sent yesterday a little clearer.
Tx isn't actually the total number aged x or greater, as I'm sure you are
aware: It's the total number of years of life remaining for the group. But
since we are only dealing with a one year period, the total "life years" is
equivalent to the population of the group.
Timothy Regan on 03/06/99 02:40:08 PM
To: "Daniel(u)Plasterer" <Daniel_Plasterer@tiginsurance.com>
cc: studygroup4a <studygroup4a@lists.casact.org>
Subject: Re: Chapter 3, Life Contingencies Stationary Population problems (T)
(Document link not converted)
I'm assuming that your question han't been answered yet since I haven't seen any
replies...
Tx is the total number aged x or greater in the population. Since the horses
must be at least age 5, Tx=5 is equal to 1000. If the horses reach the age of
20 they are imemediately sold, so Tx=20 is equal to 0.
"Daniel(u)Plasterer" <Daniel_Plasterer@tiginsurance.com> on 03/04/99 01:07:49 PM
To: studygroup4a <studygroup4a@lists.casact.org>
cc: (bcc: Timothy Regan/UUG/USA/Zurich)
Subject: Chapter 3, Life Contingencies Stationary Population problems (T)
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Fall 1992 =AA20: A ranch shows horses in competition and maintains a
constant herd size of 1,000. New horses enter at exactly age 5. No ho=
rse
leaves the herd prior to age 20 except by dying. All horses who reach =
the
age of 20 are immediately sold. Each year 100 horses die before reachi=
ng
age 20, at average age 12.
Determine how many horses are added each year using the Parmenter (AAD)=
method.
AAD=3D x + Tx - Tx+n - nlx+n
lx - lx+n
I understand how the book came up with x=3D5, n=3D15 and lx-lx+n =3D =
100, but
the part that I'm stuck on is Tx-Tx+n =3D 1,000.
Can someone please explain to me why Tx-Tx+n =3D the constant size of a=
stationary population?
I understand that Tx is the total future lifetime of those aged x in th=
e
population and Tx+n is similarly defined, but why is it that you can
subract the two and come up with the number in the population?
Any insight will be appreciated.
Dan
=
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