Leaky Pipelines

Many multi-step processes look like 'leaky pipelines', where a fractional loss/success happens at every step; such multiplicative processes can often be modeled as a log-normal distribution (or power law), with counterintuitive implications like very skewed output distributions and large final differences from small differences in per-step success rates.
bibliography⁠, statistics⁠, order-statistics
2014-11-272021-06-10 in progress certainty: highly-likely importance: 4 backlinks

  1. Someone asked if the multiple of correlated normal variables also yields a log-normal, the way ⁠; checking ⁠, I suspect not. (Experimenting with random correlation matrices generated by randcor to simulate out possible log-normals as hist(apply(abs(mvrnorm(n=500, mu=rep(0,5), Sigma=randcorr(5))), 1, prod)), the histograms look far more skewed & peaky to me than a regular log-normal—which is in accord with my intuitions about correlations between variables typicaly increasing variance and creating more extremes.)↩︎