Thursday, June 06, 2013

Unreliable friends and survival time

Mat Asher and the Unreliable Friend takes a look at survival functions.

"You can think of these curves as the chance that your friend will show up in the coming minutes, given how long you’ve already been waiting. At the very beginning of your wait, modeled by the orange curve at the far left, you can be almost certain that your friend will show up in the next 10 minutes. But by the time you’ve been waiting for 500 minutes, as seen in the blue curve at the far right, you are only 50% sure that she will show up in the next 500 minutes. Are those probabilities exact? It seems like it, but let’s zoom in on the first 25 minutes:"

My interest is whether this can be used to model time until financial crisis.  There would have to be two dimensions to the wait:  as the time expands, the intensity of the crash that ensues will be greater; as the time expands, the memory of the previous crash gets less well defined. The model has to be built up in this way with some sort of random exponential crash.  There are lots of small crashes and some major explosions.

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