## 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.$

\begin{array}{cc}

e^{-x} & x\geq 0 \\

0 & x<0 \\

\end{array}

\right.$

(1)

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.

$X=-\log U$

(2)

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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