# Slash Distribution

A probability distribution \(Slash(\mu, \sigma)\) having the PDF

If \(\mu\) is equal to zero and \(\sigma\) is equal to one then it is known as the

\[
p_{\mu, \sigma}(x) =
\begin{cases}
\dfrac{1}{2\sqrt{2\pi}\sigma} & x = \mu\\
\\
\dfrac{\phi(0) - \phi\left(\frac{x-\mu}{\sigma}\right)}{\sigma \times \left(\frac{x-\mu}{\sigma}\right)^2} & \text{otherwise}
\end{cases}
\]

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.