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Just Khan’t Get Enough
This may or may not be a surprise, given where I work, but sometimes geeky questions are asked, and geeky responses are necessary. After one such conversation regarding how many ‘a’s are canon for the imperative “Khaaan!”, I decided further investigation was necessary:
It is clear that a strong power law relation is present for low eigenkhans after the initial spike at eigenkhan 1. However, above eigenkhan 100 we enter a new realm that requires further investigation. In both power law regions we have an exponent of ~-2.68 (-2.60 for Google, -2.77 for Bing), which should be considered the canonical khansponent.
This is a slightly extended version as I have more results than I did when I wrote the first email. I can now see that the extended tail above eigenkahn 100 suggests an exponential relation, however I still do not have enough data to create a conclusive model.
In fact, this data follows a distribution known as the Pareto distribution and is related to the Bradford law of diminishing returns. In this case, the distribution has xm = 1 and α = 2.68. The expected value is, then, 1.6 with a variance of 11.12. Therefore, anything from “Kahn!” to “Kaaaaahn!” is within expectations, though there is no incorrect length.
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Better things to do with my time? Why yes, why do you ask?
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