Do you want to understand? I'll try to help, but it seems like I'm using math terminology and concepts you're not familiar with, and I don't want to presume you're interested in learning math.
Sadly, we're not even talking about the meat of my point, you got stuck on the uncontroversial preface to my real point. My point was that Nautilus is wrong and maybe being sneaky by saying that aging accelerates near the end of life because the probability of dying is going up. That's not true, and the bowling analogy shows why.
Over time, the probability of pins being knocked over goes up. But you can't conclude that the bowling ball is accelerating. The author made an incorrect conclusion from the data to make his point. It might be intentionally misleading, or it might be a mistake, but it's nonetheless incorrect to suggest that an increase in the probability of death must have been caused by an increase in the rate of aging.
I'm not saying that the PDF of death by age should be a bell curve, I'm stating a fact. It already is a bell curve. Go look at the data. You're trying to argue against reality with logic. You're right, it doesn't have to be a bell curve. But it IS a bell curve.
Very few people die of old age at 55. Many people die of old age at 80. Very few people die of old age at 100, because there are very few people left. That's a bell curve. Does that make more sense?
Sadly, we're not even talking about the meat of my point, you got stuck on the uncontroversial preface to my real point. My point was that Nautilus is wrong and maybe being sneaky by saying that aging accelerates near the end of life because the probability of dying is going up. That's not true, and the bowling analogy shows why.
Over time, the probability of pins being knocked over goes up. But you can't conclude that the bowling ball is accelerating. The author made an incorrect conclusion from the data to make his point. It might be intentionally misleading, or it might be a mistake, but it's nonetheless incorrect to suggest that an increase in the probability of death must have been caused by an increase in the rate of aging.
Now, if you want to learn the difference between CDF and PDF, look at the first two pictures in this article: https://en.wikipedia.org/wiki/Normal_distribution
I'm not saying that the PDF of death by age should be a bell curve, I'm stating a fact. It already is a bell curve. Go look at the data. You're trying to argue against reality with logic. You're right, it doesn't have to be a bell curve. But it IS a bell curve.
https://www.longevitas.co.uk/site/images/ELT15.png http://www.aihw.gov.au/uploadedImages/Subjects/Deaths/age-de... http://www.publications.parliament.uk/pa/ld200304/ldselect/l...
Very few people die of old age at 55. Many people die of old age at 80. Very few people die of old age at 100, because there are very few people left. That's a bell curve. Does that make more sense?