## Standard exponential distribution

Probability density function of the standard exponential distribution with average 1 is as follows,

$f(x)=\left\{ \begin{array}{cc} e^{-x} & x\geq 0 \\ 0 & x<0 \\ \end{array} \right.$

If $U$ is the uniform random number on $[0,1)$, it is possible to obtain a standard exponential random number $X$ with mean 1 by the following equation.

$X=-\log U$

Reference:
• JIS Z 9031:2012, Procedure for random number generation and randomization
• M.Fushimi, Random number, UP Sensho Applied Mathematics, University of Tokyo Press, 1989

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