"Mike Humphrey" wrote in message
...
On Sat, 12 Jun 2021 19:32:37 +0100, Pancho wrote:
But in this case the obvious gimmick is the actual day you were born
rather than anniversary of that day. Even if risk of death were the same
for every day lived (Poisson distribution), the day of birth would be
the most likely stopping time. The probability of surviving to
subsequent dates is monotonically declining, and hence the risk of dying
on the subsequent date is declining.

I think that's possibly what they were getting at. Assuming the chance of
death is constant (which is rather an oversimplification, as it certainly
isn't in real life), the chance of dying on each day declines
monotonically (as you can only die on a day if you didn't die on any of
the preceding days). Which leads to the rather surprising statement that,
assuming you are alive right now, you're always more likely to die today
than any later day (the probability of dying on any past day being zero,
of course).

Given this assumption, the day someone is most likely to die is the first
one, which is technically their zeroth birthday even if most people
wouldn't consider it so. Each of the following 364 days has a lower
chance of death. So of the people who die before their first birthday,
more die on the day they were born than any other day of the year.

However, the same is true of the following year - assuming they made it
to their first birthday, they either die that day or have a lower chance
of dying on each of the subsequent 364 days. So of the people who made it
to the start of their 1st birthday, more die on that birthday than on any
other day of that year.

The same applies to the year beginning on the second birthday, and each
subsequent year. Since each birthday has more deaths than the following
364 unbirthdays, when you total the deaths on each day of the year the
birthday must be the highest.

Note that I've ignored leap years, though. People who were born on
February 29th are rather unlikely to die on their birthday - which may or
may not be enough to throw the above argument. I've also assumed that the
first day of a baby's life is 24 hours long (which usually isn't the
case), and the constant chance of death each day. So actually this
probably isn't true in real life, as there's too many complications that
mean the simple mathematical model can't apply.

"Which leads to the rather surprising statement that, assuming you are alive
right now, you're always more likely to die today than any later day (the
probability of dying on any past day being zero, of course)."

Could you go over that bit again. I don't really follow your reasoning. I
would have thought the probability of dying on any given day will *increase*
for each successive day, once you get past a certain age. And even before
that age-related effect kicks in, why is your chance of dying today always
greater than the chance of dying tomorrow. Is there something that I'm not
quite understanding?

You allude to neonatal mortality in your paragraph that refers to the
"zeroth birthday". Very true. But assuming you survive this "boundary
effect", won't the chance of dying stabilise to more or less the same chance
on every date, maybe with a gradual decreasing (the theory you mention) or a
gradual increasing (for elderly people) probability as each day passes. I
don't see what is special about exactly n calendar years from your date of
birth which makes the probability of death increase on that date and
decrease again after it.

Also, in your "rather surprising statement", is that increased probability
of dying today rather than tomorrow masked by factors such a seasonal
variation in death date?

And would you expect a 10-year-old to find any of this "blindingly obvious"
to offer it as an explanation? Or anyone except a statistician to know much
about it? I *think* the guy that proposed the question was a geographer, but
I could be wrong.


In the wiki article about The Birthday Effect, it mentions that
statistically males tend to die at a greater rate just before their birthday
and females just after it. I wonder what causes that difference?