I What are the statistics of probability of dying today vs age?

[iVenky]

I don't intend to sound macabre, but I was having this thought if I have to quantify the probability of someone dying given his age (in days) how would I go about quantifying that with a minimal accuracy (ok if it's not accurate but I just need some number with days). Has anyone ever worked out this mathematical problem? What's the distribution it follows? Is it like exponential distribution?

 

[jedishrfu]

Look for some actuarial tables. This is a routine calculation for the insurance industry.

Im sure right now though those tables are influx die to Covid deaths.

 

[iVenky]

Look for some actuarial tables. This is a routine calculation for the insurance industry.

Im sure right now though those tables are influx die to Covid deaths.

Thanks for the reply. That's useful information that I didn't know before. I understand there are several factors affecting this, just curious to get an estimate. I see that the actuarial table gives the life expectancy. Do they also provide the probability of dying on a given day with age?

 

[Dale]

I don't intend to sound macabre, but I was having this thought if I have to quantify the probability of someone dying given his age (in days) how would I go about quantifying that with a minimal accuracy (ok if it's not accurate but I just need some number with days). Has anyone ever worked out this mathematical problem? What's the distribution it follows? Is it like exponential distribution?

It is definitely not an exponential distribution. An exponential distribution would be for a system like a radioactive particle that has a uniform chance of "dying" as time passes. It doesn't get older or younger so the probability doesn't change, it is always constant.

For human death and also for machinery mechanical failure the distribution is sometimes called a "bathtub" curve. There is a high risk of death/failure in the infant/break-in phase, that risk decreases to a fairly constant risk during the normal lifetime phase and then the risk of death/failure increases as the person/part reaches the end of its normal lifespan.

 

[PeroK]

I don't intend to sound macabre, but I was having this thought if I have to quantify the probability of someone dying given his age (in days) how would I go about quantifying that with a minimal accuracy (ok if it's not accurate but I just need some number with days). Has anyone ever worked out this mathematical problem? What's the distribution it follows? Is it like exponential distribution?

It also depends what other information you have about the person. Most 40-year-olds, say, who die tomorrow will already be seriously ill. The residual risk from sudden death will be much lower.

Likewise, the risk of dying during the next year will depend on long-term health factors.

If you are looking at it for yourself, then whether you take these personal factors into account or not may make a huge difference to the answer you come up with.

 

[FactChecker]

This has a column of the probability of death at a particular age and the expected remaining lifespan.

 

[PeroK]

This has a column of the probability of death at a particular age and the expected remaining lifespan.

By the time you get to 110 the outlook is a bit bleak!

 

[PAllen]

By the time you get to 110 the outlook is a bit bleak!

You still have over 40% chance of living a year or more. I like the 119 row: of the zero people living this long, 10% will live another year

 

[iVenky]

This has a column of the probability of death at a particular age and the expected remaining lifespan.

Thanks. This looks exponential. Is that right?

 

[PAllen]

Thanks. This looks exponential. Is that right?

Not remotely exponential. It validates @Dale ’s claim of a bathtub distribution. The minimum chance of dying in the next year occurs for a 10 year old. Further, not until past 50 is the chance of dying in the next year greater than it is at birth.

 

[Dale]

Thanks. This looks exponential. Is that right?

No, for an exponential distribution the Death Probability column would be constant.

 

[Frodo]

I'm using guessed numbers for demonstration.

If, say, 70% of births are alive at age 80, and 69% of births are alive at 81, then your chance of dying between 80 and 81 is 1 in 70.

If you assume the chance is equal throughout the year, then your chance of dying on a given day is 1 in 70 x 365.

You can get a better approximation by assuming that deaths are skewed towards the older people so assume a linearly increasing death rate throughout the year. For an even better approximation, fit a curve to deaths by age and calculate the chance from it.

 

[PeroK]

If, say, 70% of births are alive at age 80, and 69% of births are alive at 81, then your chance of dying between 80 and 81 is 1 in 70.

Why guess? From the tables posted earlier in this thread: if you live to 80, then the chance of dying before you reach 81 is about 4-6%, depending on whether you are male or female.

 

[Frodo]

PeroK

I was showing the method to use.

There are no single "correct values", not even in the table you cite. The numbers will vary from country to country - Chad no doubt has worse death rates than Sweden but the method is the same for both.

I think you are, as is so often the case in this forum, US isolationist and US centric - the figures are for the US. Even so, I expect they will vary from state to state and among different indigenous groups for example.

There is a whole other world out there for you to discover when you remove your blinkers.

 

[PeroK]

I think you are, as is so often the case in this forum, US isolationist and US centric - the figures are for the US.

There is a whole other world out there for you to discover when you remove your blinkers.

I'm from Scotland and live in London, actually.

 

[Frodo]

I'm from Scotland

In which case you should know that male life expectancy in the Gorbals is a mere 54, significantly lower than Iraq (67.5) and North Korea (71.4).

 

[BWV]

For laughs, the oldest known mortality table is from the reign of Justinian, as it was for annuities it did not incorporate high premodern childhood mortality (and also was biased in that presumably only relatively wealthy people with access to the full benefits of 3rd century medicine and a decent diet would ever get an annuity). Life expectancy for a 35 year old was 20 years

https://en.m.wikipedia.org/wiki/Ulpian's_life_table

 

[Dale]

There are no single "correct values", not even in the table you cite. The numbers will vary from country to country - Chad no doubt has worse death rates than Sweden but the method is the same for both.

I think you are, as is so often the case in this forum, US isolationist and US centric - the figures are for the US. Even so, I expect they will vary from state to state and among different indigenous groups for example.

There is a whole other world out there for you to discover when you remove your blinkers.

This is a bit of an overreaction. Please don't bring politics into this thread. If you don't like the US data then post whatever data you do like: contribute rather than complain. There is no need to bring in "US isolationist and US centric" comments in a non-political thread like this.

@all further political commentary will be deleted. This is a technical forum, not the GD forum.

 

[OmCheeto]

No, for an exponential distribution the Death Probability column would be constant.

Is there a name for it when the probability of dying is linear(ish) when plotted on a log scale?
At least, when ignoring the bathtub part, that is.

Coincidentally, back in August, I downloaded the file that @FactChecker referenced yesterday. Mostly in an effort to get a better understanding of all the deaths of old people during our pandemic. Hence, my ready made graphic(s).

You still have over 40% chance of living a year or more. I like the 119 row: of the zero people living this long, 10% will live another year

One of the graphs I made back in August prompted me to ask myself the question: "How do they define life expectancy?"

If 87 is the most popular age to die, then that should be how we define life expectancy, right?

It wouldn't be until yesterday that I put in the effort to figure it out.
I would explain how it's done, but it's too complicated at this time of the morning.

Anyways, the reason I bring this up, is that at age 118, my maths gets a bit buggy, and says that you should have died last year.

Not sure I've ever seen maths be rude before.

 

[FactChecker]

There are two definitions of life expectancy -- the cohort and the period life expectancy. Both are means, which is an average. The most popular age to die is the mode, not the mean. The difference is that if a small number of people live a very long time, they change the mean but not the mode.

 

[iVenky]

Not remotely exponential. It validates @Dale ’s claim of a bathtub distribution. The minimum chance of dying in the next year occurs for a 10 year old. Further, not until past 50 is the chance of dying in the next year greater than it is at birth.

Ah, I missed the small values near Age 0 when I plotted the data on excel. Got it. Thanks!