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In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate. 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 () 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. The probability density function (pdf) is : where φ(''x'') is the probability density function of the standard normal distribution.〔 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.〔(【引用サイトリンク】title=SLAPDF )〕 ==Differential equation== The pdf of the slash distribution is a solution of the following differential equation: : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Slash distribution」の詳細全文を読む スポンサード リンク
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