Generated quantites block

[bgoodri]

RNG for truncated distributions

For concreteness, I’ll give the example I worked on this morning. I want to draw from a left-truncated Weibull to impute right-censored event times. Let’s say that I want a Weibull(alpha, sigma) truncated so that my random draws are never below some lower boundary t. Then I should: (1) Figure out the quantile corresponding to lower cutoff t. Let’s say it’s 0.2, or the 20th percentile. Call that p. (2) Draw from a continuous uniform(0.2, 1). Call that draw u. (3) Apply the inverse transform f…

It is pretty much the same for the normal distribution in the sense that you first have to figure out what is the lower bound on the uniform draw which is Phi( ( 0 - mu ) / sigma ). Then inv_Phi(uniform_rng(lower_bound, 1.0)) * sigma + mu will be positive and there won’t be any rejections.