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Thread: Generating random variables

  1. #1
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    Generating random variables

    If $\displaystyle f(x)=ax^{-a-1}$ where a is positive, how do I generate random variables from a uniform random number generator? Any help would be greatly appreciated.
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  2. #2
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    Quote Originally Posted by brogers View Post
    If $\displaystyle f(x)=ax^{-a-1}$ where a is positive, how do I generate random variables from a uniform random number generator? Any help would be greatly appreciated.
    Let $\displaystyle F(x)$ be the cumulative distribution for a continuous random variable $\displaystyle X$, and let $\displaystyle Y \sim U(0,1)$. Then:

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

    has cumulative distribution $\displaystyle F(z)$.

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

    CB
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