# Application for the random variable

I am wondering if anybody knows some application for the random variable $x$ satisfying the following condition:

for $t\ge 1, a>0, c>0$

$$P(|x|\ge t)\geq \frac{c}{t^a}$$

It looks like thhis is a $p$-stable random variable, but it is not.

Any source would be very helpful.

Thank you.

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Assuming you choose $c$ such that $P(|x|\ge 1)=1$, this is the Pareto distribution with $x_m=1$. Wikipedia lists a number of empirical examples where the law is approximately satisfied. I don't know if the law ever arises naturally in a non-approximate way.
The law cannot be stable: it has a discontinuous PDF (at $t=1$) but the convolution $aX+bY$ (for $a,b\ne 0$) will always have a continuous PDF.