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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 skewed output distributions and large final differences from small differences in per-step success rates.

  1. Someone asked if the product of correlated normal variables also yields a log-normal, the way the sum of correlated normals is still normal; checking WP’s “product distribution” page, I suspect not. It will depend on the details of the correlations.

    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 typically increasing variance and creating more extremes.↩︎

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