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Relative error distributions, without the heavy tail theatrics

Nina Zumel prepared an excellent article on the consequences of working with relative error distributed quantities (such as wealth, income, sales, and many more) called “Living in A Lognormal World.” The article emphasizes that if you are dealing with such quantities you are already seeing effects of relative error distributions (so it isn’t an exotic idea you bring to analysis, it is a likely fact about the world that comes at you). The article is a good example of how to plot and reason about such situations.

I am just going to add a few additional references (mostly from Nina) and some more discussion on log-normal distributions versus Zipf-style distributions or Pareto distributions. Continue reading Relative error distributions, without the heavy tail theatrics

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Living in A Lognormal World

Recently, we had a client come to us with (among other things) the following question:
Who is more valuable, Customer Type A, or Customer Type B?

This client already tracked the net profit and loss generated by every customer who used his services, and had begun to analyze his customers by group. He was especially interested in Customer Type A; his gut instinct told him that Type A customers were quite profitable compared to the others (Type B) and he wanted to back up this feeling with numbers.

He found that, on average, Type A customers generate about $92 profit per month, and Type B customers average about $115 per month (The data and figures that we are using in this discussion aren’t actual client data, of course, but a notional example). He also found that while Type A customers make up about 4% of the customer base, they generate less than 4% of the net profit per month. So Type A customers actually seem to be less profitable than Type B customers. Apparently, our client was mistaken.

Or was he? Continue reading Living in A Lognormal World