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Weibull distribution

  1. Mar 30, 2016 #1
    1. The problem statement, all variables and given/known data
    The Weibull distribution is used frequently as a lifetime distribution and is so is used a lot in survival analysis. It can be parameterised as:##f(x;\lambda,k) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-\left(\frac{x}{\lambda}\right)^k}## for ##x\geq 0## & ##0## for ##x < 0##, where ##k > 0## is called the shape parameter and ##\lambda > 0## is called the scale parameter of the distribution.

    I have shown that it is a PDF, found the CDF, median value, Variance & failure rate. My question is how would I describe how you would generate random observations from a ##\text{Weibull}(k,\lambda)## distribution from random ##\text{Uniform}(0,1)## observations.

    2. Relevant equations


    3. The attempt at a solution
    I don't even know where to begin. Please help.
     
  2. jcsd
  3. Mar 30, 2016 #2

    andrewkirk

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    Hmm. This is something that would usually just be taught, rather than asking the student to derive it, as the answer is not terribly obvious.
    I'll try to give a hint that doesn't give the whole thing away.
    The desired random variable W will be a function of U where U is a Uniform[0,1] random variable.
    Can you think of a suitable function to use that will have the desired properties, given the functions you have worked out above and their properties, including domain and range?
     
  4. Mar 30, 2016 #3

    Ray Vickson

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    Google "Generation of random variable" or "...random variate".
     
  5. Mar 30, 2016 #4
    Oh right. I used the CDF of the Weibull distribution and noted that if ##U## is Uniform, then so is ##1-U## to get the desired result.
     
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