divorce

The statistic has nothing to do with someone born this year.

See my other post.

WRT divorce, the divorce rate in the US is approximately 1 per second
( http://www.nationmaster.com/country/us/People for 1990 data )
This is approximately half the marriage rate. If the marriage rate is
an increasing function of time over the past 20 years or so, this means
most marriages (although perhaps not most first marriages)
have ended in divorce. So Armstrong and Kristin divorcing
isn't unusual.

Dan

Ewoud Dronkert wrote:
On Sat, 6 Sep 2003 23:50:17 -0700, Dashi Toshii wrote:

A male baby born this year can expect to live for 76.3 years if he does not
die sooner!


That is incorrect. Anyone who does not die before age 76.3 either will
die at that age, or later. There are who will die in that instant,
others will live longer. So on average, all who will not die before
76.3, can expect to live longer than that.

Thanks,
E.

Daniel Connelly wrote:
The statistic has nothing to do with someone born this year.

I guess in the sense that the failure rate for light bulbs from a
particular manufacturing line has nothing to do with light bulbs
manufactured today.

WRT divorce, the divorce rate in the US is approximately 1 per second
( http://www.nationmaster.com/country/us/People for 1990 data )
This is approximately half the marriage rate. If the marriage rate is
an increasing function of time over the past 20 years or so, this means
most marriages (although perhaps not most first marriages)
have ended in divorce. So Armstrong and Kristin divorcing
isn't unusual.

Dan

This would be the case for what is (mis-) named a "stable population"
(i.e., where the age structure is an eigenvector for a matrix of birth and
death rates. In that case the eigenvalue for that matrix is the
equilibrium growth rate for the population) with fixed marriage and
divorce functions. On the one hand, the U.S. population is far from
stable, so that estimate you're making will be off; on the other, the
divorce function (the hazard rate) is steep enough that the non-stability
of the population isn't *that* important because the divorces tend to lag
the marriages by not-so-much time. That's why the ratio of the divorce
rate to the marriage rate may not be right, but it is in the right
ballpark.

Daniel Connelly wrote:
Clarification -- the statistic has to be birth-rate normalized, of
course.

So, if the probability distribution of someone being born at
time t' and dying at time t is p(t',t),
and the birth rate at time t' is r(t'), then one calculates
an effective statistic mislabeled as "life expectency", tau(t) :

/ t
|
| dt' t' p(t', t) / r(t')
|
/-infy
tau(t) = t - --------------------------
/ t
|
| dt' p(t', t)/ r(t')
|
/ -infy


Uh, Dan, this is not what life expectancy is.


However, this isn't the actual life expectency at time t, which would
be :

/ infy
|
| dt' t' p(t, t')
|
/ t
tau'(t) = -------------------- - t
/ infy
|
| dt' p(t, t')
|
/ t


Um, this isn't it, either.

However, you're right that there are two different life expectancies: one
calculated for a birth cohort (and can only be calculated after the entire
cohort has died) and the period life expectancy (which is usually what you
see printed in the newspapers), which uses the probabilities of death in
the year t for people age a (i.e., born in year t-a). If you think of a
surface where one axis is age, one axis is time, and the height of the
surface is the proportion surviving of each birth cohort, the cohort
expectation of life is the integral along the 45 degree diagonal while the
period expectation of life is the integral along the time axis.

"Daniel Connelly" wrote in message
m...
The statistic has nothing to do with someone born this year.

See my other post.

WRT divorce, the divorce rate in the US is approximately 1 per second
( http://www.nationmaster.com/country/us/People for 1990 data )
This is approximately half the marriage rate.





That sounds suspiciously like 50%.

"Robert Chung" wrote in message
...
I will WASTE my time responding to you ... but will not WASTE it
calculating a prediction on divorce ...

So then how would you know that Kurg's reference was wrong?

"projections" are not based on fact ... just theortical numbers based on
trends ... if i wanted I could bend any "projection" i wanted based on the
sample ... don't be ignorant all your life.

BTW, it's 4 anyway ...

4% ??? Wow, you *are* a dumbass.

and you are not?? if you were not one you would have known the movie
reference;-) Did you see a % sign ...

s
http://boardnbike.com

Robert Chung wrote:
Daniel Connelly wrote:

The statistic has nothing to do with someone born this year.


I guess in the sense that the failure rate for light bulbs from a
particular manufacturing line has nothing to do with light bulbs
manufactured today.


WRT divorce, the divorce rate in the US is approximately 1 per second
( http://www.nationmaster.com/country/us/People for 1990 data )
This is approximately half the marriage rate. If the marriage rate is
an increasing function of time over the past 20 years or so, this means
most marriages (although perhaps not most first marriages)
have ended in divorce. So Armstrong and Kristin divorcing
isn't unusual.

Dan


This would be the case for what is (mis-) named a "stable population"
(i.e., where the age structure is an eigenvector for a matrix of birth and
death rates. In that case the eigenvalue for that matrix is the
equilibrium growth rate for the population) with fixed marriage and
divorce functions. On the one hand, the U.S. population is far from
stable, so that estimate you're making will be off; on the other, the
divorce function (the hazard rate) is steep enough that the non-stability
of the population isn't *that* important because the divorces tend to lag
the marriages by not-so-much time. That's why the ratio of the divorce
rate to the marriage rate may not be right, but it is in the right
ballpark.



The divorce rate after 10 years of marriage is around 33%:
http://www.skfriends.com/do-43-perce...es-divorce.htm

So a time slice isn't sufficient.

Dan

Daniel Connelly wrote:
Robert Chung:
Uh, Dan, this is not what life expectancy is.

What's the formula, then?

There are several formulas, but the two that are easiest to understand use
either the probability of survivorship to a particular age or the hazard
function.

Let p(a,t+a) = the probability of surviving to age a at time t. Note that
p(0,t) = 1 and p(omega, t+omega) = 0 where omega is a big number like 116
or so (unless you believe in the literal interpretation of the bible, in
which case you may think that omega is 989).

Then the cohort expectation of life (aka the lifetable expectation of
life) is:
int [from 0 to omega] p(x,t+x) dx

The period expectation of life is what you've been complaining about. It's
based on a "virtual" cohort where you use p(x,today) in place of p(x,t+x).

If you use the hazard function, p(a,t) = exp ( - int [0 to a] mu(x,t) dx
and then you can proceed as before.

Your first formula was actually pretty close to the average age of death
in a population (but I confess I have a hard time reading ascii formulas
so I may be slightly off), but except in a stable population with a zero
growth rate, that's not the expectation of life. Your second formula is
even closer, but I think you're subtracting off a t at the end and I can't
figure out why. BTW,


Um, this isn't it, either.

However, you're right that there are two different life expectancies:
one calculated for a birth cohort (and can only be calculated after
the entire cohort has died) and the period life expectancy (which is
usually what you see printed in the newspapers), which uses the
probabilities of death in the year t for people age a (i.e., born in
year t-a). If you think of a surface where one axis is age, one axis
is time, and the height of the surface is the proportion surviving of
each birth cohort, the cohort expectation of life is the integral
along the 45 degree diagonal while the period expectation of life is
the integral along the time axis.



Right. But neither is the "expectation value of the time to death of
a baby born now", which is commonly reported.

It's no more wrong than saying that the expected value of a random
variable X is E(X) without specifying the pdf. We do this all the time
when we estimate things using weighted means, or weighted least squares,
or any kind of weighting scheme. Demographic measures are concpetually
simpler to understand when they pertain to cohorts, but they are certainly
more useful when they pertain to periods. The period life expectancy uses
the survivorships or the death probabilities for *this* period.

Robert Chung wrote:
Daniel Connelly wrote:

Robert Chung:

Uh, Dan, this is not what life expectancy is.

What's the formula, then?


There are several formulas, but the two that are easiest to understand use
either the probability of survivorship to a particular age or the hazard
function.

Let p(a,t+a) = the probability of surviving to age a at time t. Note that
p(0,t) = 1 and p(omega, t+omega) = 0 where omega is a big number like 116
or so (unless you believe in the literal interpretation of the bible, in
which case you may think that omega is 989).

Then the cohort expectation of life (aka the lifetable expectation of
life) is:
int [from 0 to omega] p(x,t+x) dx

Right. That's essentially what I wrote. But p(x, t+x) can't be evaluated
for x0, which is in the future for a contemporary evaluation.


The period expectation of life is what you've been complaining about. It's
based on a "virtual" cohort where you use p(x,today) in place of p(x,t+x).


Exactly. Not the same. I believe my function was equivalent.

If you use the hazard function, p(a,t) = exp ( - int [0 to a] mu(x,t) dx
and then you can proceed as before.

Right. Hazard functions aren't so simple, however. Nor are they
time-invariant.


Your first formula was actually pretty close to the average age of death
in a population (but I confess I have a hard time reading ascii formulas
so I may be slightly off), but except in a stable population with a zero
growth rate, that's not the expectation of life. Your second formula is
even closer, but I think you're subtracting off a t at the end and I can't
figure out why. BTW,


My scalar field was the probability of living from time t to t', where
times are absolute, so you need to subtract the current time to get an
age.

Daniel Connelly wrote:
So a time slice isn't sufficient.

Yeah, and that's why no serious researcher would do it that way. I was
just explaining why when you do the cross-sectional (aka time slice) thing
you get a number in the right ballpark rather than a number like .01 or
1.0.

I often do cocktail party calculations like that. I call them cocktail
party calculations because unlike Back Of The Envelope calculations you do
them while leaning against a wall with a drink in your hand (occasionally
with a slight buzz). BOTE is one step up because you actually get to use a
pencil.