Simulate Times to Failure from Right Censored data

[Konrad-H]

Is there a way to simulate random times until failure event from a fitted distribution taking into account the time it already passed?

I couldn't find it in the documentation. Thank you!

[CamDavidsonPilon]

Hi @Konrad-H - there is something that you can use. Give a fitted univariate model f, you can provide uniform random variates to the percentile function:

wf = WeibullFitter()
T = np.random.exponential(4, size=1000)
wf.fit(T)
sim = wf.percentile(np.random.random(size=10000)) # simulate 10000 survival times

This works due to inverse transform sampling.

Now, you want to take into account time that has already passed, call this time s. For this, you just need to remove any entries below s in the resulting vector.

sim[sim > s]

[Konrad-H]

Hi!
Really thank you for your answer!
I thought about your answer and something doesnt quite add up to me.
By the definition of conditional probability $P(T<x | T>t) = P(T<x & T>t)/P(T>t)$.
Anyway, the (bootstrapped) fit parameters and histograms are the same for the Conditional method so I believe there has to be an error in my thought process.

[CamDavidsonPilon]

Take a look at this answer first for a derivation of the conditional survival function: https://stats.stackexchange.com/questions/519773/remaining-useful-life-for-weibull-distributed-lifetimes/519902#519902

Point is that the conditional survival function is just a rescaled version of the original survival function, so sampling from the conditional should be identical to sampling from the original.

[Konrad-H]

Ok! Everything is crystal clear now! 🤩