Generating random variables

**brogers** · January 30th 2010, 08:48 PM

If $f(x)=ax^{-a-1}$ where a is positive, how do I generate random variables from a uniform random number generator? Any help would be greatly appreciated.

**CaptainBlack** · January 30th 2010, 11:41 PM

Originally Posted by brogers

If $f(x)=ax^{-a-1}$ where a is positive, how do I generate random variables from a uniform random number generator? Any help would be greatly appreciated.

Let $F(x)$ be the cumulative distribution for a continuous random variable $X$ , and let $Y \sim U(0,1)$ . Then:

$Z=F^{-1}(Y)$

has cumulative distribution $F(z)$ .

Hence if $y$ is a sample from the $U(0,1)$ , $z=F^{-1}(y)$ is a sample from the distribution with cumulative distribution $F(z)$

CB

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