# simulate conditional Weibull conditional on survival > T ---------------

# reliability function is exp{-(T+t/b)^a} / exp{-(T/b)^a} = 1-F(t)

# n = number of points to return

# shape = shape parm of weibull

# scale = scale parm of weibull (default 1)

# t is minimum (default is 0, which makes the function act like rweibull)

my_rweibull <- function(n,shape,scale=1,t=0) {

if (length(t)!=1 && length(t)!=n) {

stop("length(t) is not 1 or n")

}

return(scale*(-log(runif(n))+(t/scale)^shape)^(1/shape))

}

You use this function just like rweibull, with the exception that you pass in another vector t of minimum times or a scalar representing the minimum time of all simulated values. The idea is that the probability that the random variable will be at least T is given by exp{-(T+t/b)^a} / exp{-(T/b)^a}, so you can simulate this with a uniform random variate. I use the inversion method on the reliability function (just like using the inversion method on the distribution function, with the insight that if U is uniform(0,1), so is 1-U).

Truth be told, I ought to buckle down and learn how to do packages in R, but for now I'll just pass on some code on my blog if I think it will be helpful (or if I need to find it while doing a Google search later).

(Edit on 7/16:

**OOPS!**A previous version of this had the scale and shape parameters switched. I've corrected it now. If you copied this before 7/16/2016, please check again.)