Slash Distribution

A probability distribution \(Slash(\mu, \sigma)\) having the PDF
\[ p_{\mu, \sigma}(x) = \begin{cases} \dfrac{1}{2\sqrt{2\pi}\sigma} & x = \mu\\ \\ \dfrac{\phi(0) - \phi\left(\frac{x-\mu}{\sigma}\right)}{\sigma \times \left(\frac{x-\mu}{\sigma}\right)^2} & \text{otherwise} \end{cases} \]
where \(\phi_{\mu,\sigma}\) is the normal PDF with mean \(\mu\) and standard deviation \(\sigma\).
If \(\mu\) is equal to zero and \(\sigma\) is equal to one then it is known as the standard slash distribution and governs the ratio of independent standard normal and uniform random variables.