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Fat-tailed distributions

August 8th, 2012, 8:51am by Sam Wang

Attention geeks: As detailed yesterday, I am pondering how to address the issue of black-swan events. It seems to me that the correct approach is not to assume a larger value for the Meta-analysis standard deviation (MMSD), but to use a distribution that has fatter tails.

I am currently considering using the t-distribution. For instance, the t-distribution for a 2.0-sigma lead and 3 degrees of freedom gives tcdf(2.0,3) = 0.93, a 93% win probability. The normal distribution gives normcdf(2.0,0,1) = 97.7%. (Recall that I very roughly estimated the black-swan frequency as about 8%.)

Under current conditions, the re-elect probability would then be tcdf(3.0/2.2,3) = tcdf(1.36,3) = 87%.

One Comment so far ↓

• Hello Mr. Wang,

I came across a few interesting pieces on fat-tailed distributions while doing research on bankruptcy models:

I also considered the possibility of utilizing the student-t distribution. What are your thoughts?

Matt