In some work I was doing I derived a probability distribution that I do not recognize. Is it a known distribution?
$\Pr(X\le x)=\exp\left[-\frac{1}{2}\left(\frac{1}{2}x-\sqrt{1+\frac{x^{2}}{4}}\right)^{2}\right]$
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$\begingroup$ That square root reminds me of the Wigner semicircle distribution. You might try seeing if there is some nice transformation that takes you to it. $\endgroup$– Steve HuntsmanCommented Jan 11, 2012 at 14:45
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$\begingroup$ The square root in my distribution comes from a hyperbola. The x/2 term flattens the positive-x asymptote against the x-axis, and the exponential maps 0 (well, $-\delta$) to 1 (or rather, $1-\epsilon$). $\endgroup$– CyanCommented Jan 11, 2012 at 15:41
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2$\begingroup$ Can I assume you've already looked through the Johnson, Kotz & Balakrishnan volumes? $\endgroup$– cardinalCommented Jan 12, 2012 at 23:31
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