PDF from difference of two Weibull distributions How should I derive a PDF from the difference of a couple of given two parameter Weibull distributions ? The convolution integrals become very difficult to evaluate. PS : The parameters are not necessarily the same since the idea is to get a distribution for a general case. 
 A: This seems to be a difficult question. I tried to find a closed form answer with the help of maple, but maple gives up!  So I will use the same numerical approach as used in Difference of two i.i.d. lognormal random variables.  The convolution formulas used are developed there, so will not be redone here.  If $X, Y$ are independent weibull distributed (possibly with different parameters) then the density of $D=X-Y$ is 
$$
   f_D(t) = \int_0^\infty f(t+y) g(y) \; dy
$$
with $f$ the density of $X$, $g$ the density of $Y$.
The density of the difference $D$ can then be calculated via numerical integration:
dDIFF <-  function(x, shape1, shape2=shape1, scale1=1, scale2=scale1) {
    res  <- x
    for (xx in seq(along=x)) {
        res[xx]  <-  integrate(function(y) dweibull(y+x[xx], shape1, scale1) * dweibull(y, shape2, scale2),  lower=0.0,  upper=+Inf)$value
    }
    return(res)
    }

and we can make a plot of that, first in a symmetrical case:  

(note the cusp at zero), and then an asymmetrical case:  

This numerical solution is very fast and should be enough for most practical purposes!  If you have to evaluate it very often, maybe make a spline approximation?
