Every so often you hear about the oldest person in the world dying. On April 1st, Elsi Calvert Thompson, America’s oldest person, died at 114. On December 17th, 2012, the 115-year-old Dina Mandredini passed away, handing off the world’s oldest living person title to Besse Cooper. But how often does the world’s oldest person die?
If you live in a country with Ncountry people, a continent with Ncontinent people and a world with Nworld people, during a year and on average, how often will you be notified (if you’re paying attention to your quality tabloid) of the death of the oldest man/woman/person alive of your country/continent/world? (Note that a death will result in at most one notification.)
On Stackexchange, which calls itself “a question and answer site for people studying math at any level,” Marc van Leeuwen tried to answer that question, and with the help from the community, came up with lots of ways to think about it.
Mortality tables from the CDC, for example, give one answer, provided by Chris Taylor. These tables only go up to 100, and since many of the oldest people crack that ceiling, he had to extrapolate a bit, knowing that the oldest person to have ever lived died at 122.
For each age a, the number of people of age a in year t is the fraction of the population aged a−1 at time t−1 who don’t die, i.e.N(t,a) (1−h(a−1))×N(t−1,a−1)
Eventually, he had an answer:
Taking the total number of events, and dividing by the number of years that I run the simulation for, gives an approximate rate. The punchline is that in my simulation, I see 15,234 events in 10,000 years, for an approximate rate of once in every 0.66 years.
Another person looked to the Gerontology Research Group, who keeps records on the death of the oldest living person. A user named Gwern calculated:
I extracted the final column, death dates, and formatted it and extracted the intervals between the death dates of each person, reasoning that if the Oldest Person In The World who died in 1955 is succeeded by a person who died in 1956, that meant an observer would, in 1955, wait ~1 year for the new Oldest Person to die. The mean interval between deaths turns out to be 1.2 years, but the median wait turns out to be 0.65 years! This seems to be due in large part due to the astounding lifespan of Jeanne Calment, as you will see on the interval graph shortly.
At Stackexchange, a few more people came up with answers, but things seem to settle around one oldest-person death every 0.65 years. Now, obviously, figuring out who the oldest person in the world is, is pretty hard. But since most of us will never hold the title of oldest person in the world, we can at least savor the fact that, for at least a few seconds, we were at one point the youngest.
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