Unexpected behavior when using "pexp" function within RTMB likelihood and "log.p = TRUE"

[pthomp...@gmail.com]

Hi there,

I'm building a model with RTMB that requires me to use the "pexp" (i.e., cumulative distribution function) function within the negative log-likelihood (not just "dexp" as is usually used). A simplified version of the model I'm working on is effectively a truncated exponential distribution, of which I provide an example below:

library(RTMB)

N = 1e6
L = 1
Q = 0.75

t_max = qexp(Q, rate = L)

# Generate some exponential data that are artificially truncated
DAT = data.frame(tt = rexp(N, rate = L)) |>
  dplyr::mutate(tt < t_max)

trunc_exp = function(pars, dat = DAT) {
 
  "[<-" <- ADoverload("[<-")
  getAll(pars, dat, warn = FALSE)
 
  # Negative log-likelihood for truncated exponential distribution
  nll_begin = -dexp(tt, exp(lambda_log), log = TRUE)

  # Account for the truncation factor to normalize the probabilities
  nll_weight = RTMB::pexp(t_max, exp(lambda_log), log.p = TRUE)
 
  sum(nll_begin + nll_weight)
 
}

obj = RTMB::MakeADFun(trunc_exp, list(lambda_log = 0))

For me, the final line (making the RTMB model object) throws an error: "Error in RTMB::pexp(t_max, exp(lambda_log), log.p = TRUE) : Non-numeric argument to mathematical function". I tested this out and it turns out the error goes away when you remove the "log.p = TRUE" argument. I'm not sure what the problem is because if you just call the "trunc_exp()" function in R, it works and returns what you'd expect. I've tried a bunch of things but can't seem to figure out how to fix this. Hopefully it's something easy & obvious!

An easy workaround for this is to simply use log(pexp(...)) instead, but this isn't ideal as I believe it's less precise than doing the log calculation inside the pexp() function.

I'm using R 4.5.3 on Windows 11 with RTMB version 1.9 (TMB version 1.9.21).

Let me know if you have any questions and thank you in advance for your help!

Peter R. Thompson, Ph.D.