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Has anyone seen the following quantity come up in the literature?

$$\frac{\mathbb{E}[X]^2}{\mathbb{E}[X^2]}$$

I saw it in equation 10 of this paper.

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5  
I don't think it has a name, but, sure, it shows up on occasion. Here is one case: Let $X$ be a nonnegative random variable in $L_2$. Then, $\mathbb P(X > 0) \geq (\mathbb EX)^2 / \mathbb EX^2$. This is a straightforward consequence of Cauchy-Schwarz. – cardinal Dec 5 '12 at 1:28
1  
I suppose one could write the quantity as $$\frac{1}{1+(\sigma/\mu)^2} = \frac{1}{1+C^2}$$ where $C = \sigma/\mu$ is called the coefficient of variation. – Dilip Sarwate Mar 12 '13 at 23:03
    
The paper you linked to has been revised. What once was equation 10 is now equation 7. – Joel Reyes Noche Aug 5 '13 at 5:16

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