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There is no such thing as an 'exponential curve' in our finite world. And the derivative of the sigmoid is a bell curveish thing.
by yters 7y ago
There is no such thing as an 'exponential curve' in our finite world. And the derivative of the sigmoid is a bell curveish thing.
- Gravityloss 7y agoPiecewise. A exponential forecast may be a better model for example for policy making on some time period than a linear one would be.
- littlestymaar 7y agoIt's a logistic function, which is different from the “bell curve”. They look pretty much the same, but their mathematical properties are really different so they should not be confused.
- CrazyStat 7y agoThe left tail of a sigmoid looks a hell of a lot like an exponential. The left tail of the derivative of a sigmoid also looks like an exponential.
- tlarkworthy 7y agoYes, thats why exponential curves taper off to an S-curve in the real world (e.g. population growth is exponential at first, then tapers off when hitting food limits). This article is about estimating the more realistic s-curve in the real world. The point it: You cannot get a sense of the end by observing the beginning... even in the super idealized case of the data coming from a perfect s-curve, let alone the real world. Its a great article.
- empath75 7y agoWhen you’re talking about a highly contagious disease it’s more or less a distinction without a difference. It’s exponential until very close to the point where a significant percentage of the vulnerable population is infected. It’s not super interesting to point out that it’s no longer growing exponentially, when half the population has it already.
- yters 7y agoIt is interesting to think about how long the exponential trend will continue before becoming a sigmoid.