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Math Help - Generating random variables

  1. #1
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    Generating random variables

    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.
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  2. #2
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    Quote Originally Posted by brogers View Post
    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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