Use the inverse transformation method to present an approach for generating a random variable from the Weibull distribution $$F(t)=1-e^{-a t^{\beta}} \quad t \geq 0$$
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Step 1
Step 1:** Find the inverse of the Weibull distribution function $F(t)$: $$F(t) = 1 - e^{-at^{\beta}}$$ To find the inverse, set $F(t) = u$ and solve for $t$: $$u = 1 - e^{-at^{\beta}}$$ $$e^{-at^{\beta}} = 1 - u$$ $$-at^{\beta} = \ln(1 - u)$$ $$t^{\beta} = Show more…
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