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Someone gave me a formula at work to use, but I have never seen it before.

It is (sum of squares) divided by ((sum of absolute values) squared): $$ \frac{\displaystyle\sum_i y_i^2}{\left(\displaystyle\sum_i \mid y_i \mid\right)^2} $$ So for example if you had two points -2 and 1, the statistic value would be 5/9

Does anyone know if this statistic has a name?

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    $\begingroup$ What exactly is your question? $\endgroup$
    – Tim
    Commented Feb 15, 2020 at 22:04
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    $\begingroup$ What's the context? Without any, it's just a formula for (sum of squares) divided by ((sum of absolute values) squared). $\endgroup$
    – corey979
    Commented Feb 15, 2020 at 22:06
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    $\begingroup$ Without context, likely the most we can do is give a mathematical description and name some properties. For instance, putting the values into an $n$-vector $x,$ this is the square of the ratio of the $L^2$ and $L^1$ norms of $x,$ $\left(|x|_2/|x|_1\right)^2.$ It must lie in the interval $[1/n,1].$ The lower limit is achieved when all the values of $x$ are equal (and nonzero); the upper limit is reached when all but one of the values is zero. $\endgroup$
    – whuber ♦
    Commented Feb 15, 2020 at 22:18
  • $\begingroup$ I think he is just asking for the name of this statistic (if it has one). $\endgroup$
    – Peter Flom
    Commented Feb 16, 2020 at 15:08
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    $\begingroup$ @Peter Although that's the overt purpose, asking the name of something is not of statistical interest and rarely is the ultimate objective. One asks the name in order to find out something more. Often any mathematically useful quantity, if it has a name, has more than one because it has been invented by different communities or has multiple applications. Thus, answering even the simple "what is the name of" question can be informed by information about the underlying purpose. $\endgroup$
    – whuber ♦
    Commented Apr 8, 2020 at 14:14

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Statistic to detect monopoly formation

I agree with the comments that without any context, it's just a formula for (sum of squares) divided by ((sum of absolute values) squared). Still, out of curiosity, I tried to think of possible contexts where such a formula would serve a purpose:

As this formula somehow reminded me of Shannon entropy and the phrase "someone gave me formula at work to use" created the association of ecology (personal experience with ecologists), I somehow had the intuition that this formula would describe or evaluate monopolies.

So, I searched the net for "monopoly formula" and immediately found this Herfindahl–Hirschman Index!

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