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Template:Probability distribution In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate.[1] In other words, if the random variable Z has a normal distribution with zero mean and unit variance, the random variable U has a uniform distribution on [0,1] and Z and U are statistically independent, then the random variable XZ / U has a slash distribution. The slash distribution is an example of a ratio distribution. The distribution was named by William H. Rogers and John Tukey in a paper published in 1972.[2]

The probability density function is

where φ(x) is the probability density function of the standard normal distribution.[3] The result is undefined at x = 0, but the discontinuity is removable:

The most common use of the slash distribution is in simulation studies. It is a useful distribution in this context because it has heavier tails than a normal distribution, but it is not as pathological as the Cauchy distribution.[3]

References

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  2. Template:Cite doi
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