![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/b/b3/Slashpdf.svg/640px-Slashpdf.svg.png&w=640&q=50)
Slash distribution
From Wikipedia, the free encyclopedia
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 X = Z / 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]
Probability density function ![]() | |||
Cumulative distribution function ![]() | |||
Parameters | none | ||
---|---|---|---|
Support |
| ||
| |||
CDF |
| ||
Mean | Does not exist | ||
Median | 0 | ||
Mode | 0 | ||
Variance | Does not exist | ||
Skewness | Does not exist | ||
Excess kurtosis | Does not exist | ||
MGF | Does not exist | ||
CF |
|
The probability density function (pdf) is
where is the probability density function of the standard normal distribution.[3] The quotient 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]