Weibull Distribution

• pdf
  
  $$f(x) = \left\{ \begin{array}{ll} \frac{\beta}{\alpha^{\beta}... ...^\beta, & x \ge 0 \\ 0, & otherwise \\ \end{array} \right.$$
  
  

• Steps:

  Step 1.

  cdf
  

  $$F(x) = 1 - {e^{-(x/\alpha)}}^\beta$$

  
  

  for $x \ge 0$

  Step 2.

  let $F(x) = 1 - {e^{-(x/\alpha)}}^\beta = R$

  Step 3.

  Solve for $X$ in terms of $R$ yields
  

  $$X = \alpha [ -ln (1 - R)]^{1/\beta}$$

  
  

  Step 4.

  Generate uniformly distributed $R_i$ from (0,1) feeding them to the function in Step 3 to get $X$.