Expand marginal model distribution support

[seabbs]

In #426 support was added for Weibull, Lognormal, and Gamma. primarycensored supports many more distributions that this so we can extend this. This will be easier if we wait for epinowcast/primarycensored#175

Once this has been completed we can support everything that primarycensored supports but our posterior prediction and R side log lik will be limited to distributions where brms uses an internal log_lik_censor call. I think to close this issue we should document what those are and open a new issue for extending support.

[athowes]

limited to distributions where brms uses an internal log_lik_censor call

How easy would these be to implement and submit as PRs to brms?

[seabbs]

they are all internal functions and I have no idea

[athowes]

https://github.com/paul-buerkner/brms/blob/2e5177a7df2bbdf699ac71f04dbaab8fdb9ca3da/R/log_lik.R#L990 seems to look quite a generic solution?

# ----------- log_lik helper-functions -----------
# compute (possibly censored) log_lik values
# @param dist name of a distribution for which the functions
#   d<dist> (pdf) and p<dist> (cdf) are available
# @param args additional arguments passed to pdf and cdf
# @param prep a brmsprep object
# @return vector of log_lik values
log_lik_censor <- function(dist, args, i, prep) {
  pdf <- get(paste0("d", dist), mode = "function")
  cdf <- get(paste0("p", dist), mode = "function")
  y <- prep$data$Y[i]
  cens <- prep$data$cens[i]
  if (is.null(cens) || cens == 0) {
    x <- do_call(pdf, c(y, args, log = TRUE))
  } else if (cens == 1) {
    x <- do_call(cdf, c(y, args, lower.tail = FALSE, log.p = TRUE))
  } else if (cens == -1) {
    x <- do_call(cdf, c(y, args, log.p = TRUE))
  } else if (cens == 2) {
    rcens <- prep$data$rcens[i]
    x <- log(do_call(cdf, c(rcens, args)) - do_call(cdf, c(y, args)))
  }
  x
}