Ratio Distribution - Ratio of Standard Normal To Standard Uniform

Ratio of Standard Normal To Standard Uniform

If X has a standard normal distribution and Y has a standard uniform distribution, then Z = X / Y has a distribution known as the slash distribution, with probability density function

$p_Z(z) = \begin{cases} \left / z^2 \quad & z \ne 0 \\ \phi(0) / 2 \quad & z = 0, \\ \end{cases}$

where φ(z) is the probability density function of the standard normal distribution.

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