Cumulative Distribution Function of Sum two Weibull random variables

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If $Y_0$ and $Y_1$ both have Weibull distribution i.e. $Y_0 \sim Weibull(\lambda_0,\beta_0)$ and $Y_1 \sim Weibull(\lambda_1,\beta_1)$ then what will be cumulative density function of $Y_0+Y_1$, i.e. $$\Pr(Y_0+Y_1<y)=\int_0^\infty \Pr(Y_0<y-z|z=Y_1)f_{Y_1}(Y_1)\ dY_1$$