diff --git a/NAMESPACE b/NAMESPACE
index 680601a1..bf0d7dc7 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -38,6 +38,7 @@ export(dev_binom)
 export(dev_gamma)
 export(dev_gamma_pois)
 export(dev_gamma_pois_zi)
+export(dev_gamma_pois_zt)
 export(dev_lnorm)
 export(dev_neg_binom)
 export(dev_norm)
@@ -67,6 +68,7 @@ export(log_lik_exp)
 export(log_lik_gamma)
 export(log_lik_gamma_pois)
 export(log_lik_gamma_pois_zi)
+export(log_lik_gamma_pois_zt)
 export(log_lik_lnorm)
 export(log_lik_neg_binom)
 export(log_lik_norm)
@@ -106,6 +108,7 @@ export(ran_binom)
 export(ran_gamma)
 export(ran_gamma_pois)
 export(ran_gamma_pois_zi)
+export(ran_gamma_pois_zt)
 export(ran_lnorm)
 export(ran_neg_binom)
 export(ran_norm)
@@ -120,6 +123,7 @@ export(res_binom)
 export(res_gamma)
 export(res_gamma_pois)
 export(res_gamma_pois_zi)
+export(res_gamma_pois_zt)
 export(res_lnorm)
 export(res_neg_binom)
 export(res_norm)
diff --git a/NEWS.md b/NEWS.md
index f34816fb..52a4a3aa 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -2,6 +2,7 @@
 
 # extras 0.8.0.9001
 
+- Added `log_lik_gamma_pois_zt()`, `dev_gamma_pois_zt()`, `ran_gamma_pois_zt()`, and `res_gamma_pois_zt()` for the zero-truncated gamma-Poisson (negative binomial) distribution.
 - Added `log_lik_exp()`.
 - Added `log_lik_beta()`.
 - Added 'log_lik_unif()'.
diff --git a/R/dev.R b/R/dev.R
index 4c2d17b1..1a5f52e5 100644
--- a/R/dev.R
+++ b/R/dev.R
@@ -244,6 +244,62 @@ dev_gamma_pois_zi <- function(x, lambda = 1, theta = 0, prob = 0, res = FALSE) {
   dev_res(x, lambda * (1 - prob), dev)
 }
 
+#' Zero-Truncated Gamma-Poisson Deviances
+#'
+#' Saturated log-likelihood is found numerically per observation since the
+#' truncated likelihood has no closed-form maximum.
+#'
+#' @inheritParams params
+#' @param x A whole numeric vector of values greater than or equal to 1.
+#'
+#' @return An numeric vector of the corresponding deviances or deviance residuals.
+#' @family dev_dist # make live when complete
+#' @export
+#'
+#' @examples
+#' dev_gamma_pois_zt(c(1, 3, 4), 3, 2)
+dev_gamma_pois_zt <- function(x, lambda = 1, theta = 0, res = FALSE) {
+  force(x)
+  args_not_na <- !is.na(x + lambda + theta)
+  if (length(theta) == 1) {
+    theta_vec <- theta
+  } else {
+    theta_vec <- theta[args_not_na]
+  }
+  opt_lambda <- rep(NA_real_, length(args_not_na))
+  if (any(args_not_na)) {
+    upper <- max(x[args_not_na])
+    if (!is.finite(upper) || upper <= 0) upper <- 1
+    opt_lambda[args_not_na] <- parallel_optimize(
+      f = make_opt_gamma_pois_zt(x[args_not_na], theta_vec),
+      interval = c(.Machine$double.eps, upper),
+      N = sum(args_not_na)
+    )
+  }
+  dev1 <- log_lik_gamma_pois_zt(x = x, lambda = opt_lambda, theta = theta)
+  dev2 <- log_lik_gamma_pois_zt(x = x, lambda = lambda, theta = theta)
+  dev <- dev1 - dev2
+  dev[!is.na(dev) & dev < 0 & dev > -1e-7] <- 0
+  dev <- dev * 2
+  if (vld_false(res)) {
+    return(dev)
+  }
+  log_p0 <- dnbinom(0, mu = lambda, size = 1 / theta, log = TRUE)
+  trunc_mean <- lambda / -expm1(log_p0)
+  dev_res(x, trunc_mean, dev)
+}
+
+# Objective function for optimization.
+make_opt_gamma_pois_zt <- function(x, theta) {
+  force(x)
+  force(theta)
+  function(lambda) {
+    out <- -log_lik_gamma_pois_zt(x = x, lambda = lambda, theta = theta)
+    out[is.nan(out)] <- Inf
+    out
+  }
+}
+
 #' Log-Normal Deviances
 #'
 #' @inheritParams params
diff --git a/R/log-lik.R b/R/log-lik.R
index 9b2cfe72..c9563dfa 100644
--- a/R/log-lik.R
+++ b/R/log-lik.R
@@ -205,6 +205,23 @@ log_lik_gamma_pois_zi <- function(x, lambda = 1, theta = 0, prob = 0) {
   log(lpois)
 }
 
+#' Zero-Truncated Gamma-Poisson Log-Likelihood
+#'
+#' @inheritParams params
+#' @param x A whole numeric vector of values greater than or equal to 1.
+#'
+#' @return An numeric vector of the corresponding log-likelihoods.
+#' @family log_lik_dist
+#' @export
+#'
+#' @examples
+#' log_lik_gamma_pois_zt(c(1, 3, 4), 3, 1)
+log_lik_gamma_pois_zt <- function(x, lambda = 1, theta = 0) {
+  log_lik <- dnbinom(x, mu = lambda, size = 1 / theta, log = TRUE)
+  log_p0 <- dnbinom(0, mu = lambda, size = 1 / theta, log = TRUE)
+  log_lik - log1p(-exp(log_p0))
+}
+
 #' Log-Normal Log-Likelihood
 #'
 #' @inheritParams params
diff --git a/R/ran.R b/R/ran.R
index 8c659585..d2f9f4b7 100644
--- a/R/ran.R
+++ b/R/ran.R
@@ -97,6 +97,40 @@ ran_gamma_pois_zi <- function(n = 1, lambda = 1, theta = 0, prob = 0) {
   ran_neg_binom(n = n, lambda = lambda, theta = theta) * ran_bern(n, prob = 1 - prob)
 }
 
+#' Zero-Truncated Gamma-Poisson Random Samples
+#'
+#' Drawn via rejection sampling so all returned values are at least 1.
+#'
+#' @inheritParams params
+#' @return A numeric vector of the random samples.
+#' @family ran_dist
+#' @export
+#'
+#' @examples
+#' ran_gamma_pois_zt(10, lambda = 3, theta = 1)
+ran_gamma_pois_zt <- function(n = 1, lambda = 1, theta = 0) {
+  chk_whole_number(n)
+  chk_gte(n)
+  if (n == 0) {
+    return(integer(0))
+  }
+  lambda <- rep_len(lambda, n)
+  theta <- rep_len(theta, n)
+  out <- integer(n)
+  remaining <- seq_len(n)
+  while (length(remaining) > 0) {
+    draws <- as.integer(stats::rnbinom(
+      length(remaining),
+      mu = lambda[remaining],
+      size = 1 / theta[remaining]
+    ))
+    accepted <- draws > 0
+    out[remaining[accepted]] <- draws[accepted]
+    remaining <- remaining[!accepted]
+  }
+  out
+}
+
 #' Log-Normal Random Samples
 #'
 #' @inheritParams params
diff --git a/R/res.R b/R/res.R
index a1f1496a..f6119522 100644
--- a/R/res.R
+++ b/R/res.R
@@ -173,6 +173,37 @@ res_gamma_pois_zi <- function(x, lambda = 1, theta = 0, prob = 0, type = "dev",
   )
 }
 
+#' Zero-Truncated Gamma-Poisson Residuals
+#'
+#' Centred on the truncated mean and standardised by the truncated variance.
+#'
+#' @inheritParams params
+#' @param x A whole numeric vector of values greater than or equal to 1.
+#'
+#' @return An numeric vector of the corresponding residuals.
+#' @family res_dist
+#' @export
+#'
+#' @examples
+#' res_gamma_pois_zt(c(1, 2, 5), 2, 1)
+res_gamma_pois_zt <- function(x, lambda = 1, theta = 0, type = "dev", simulate = FALSE) {
+  chk_string(type)
+  if (!vld_false(simulate)) {
+    x <- ran_gamma_pois_zt(length(x), lambda = lambda, theta = theta)
+  }
+  log_p0 <- dnbinom(0, mu = lambda, size = 1 / theta, log = TRUE)
+  one_minus_p0 <- -expm1(log_p0)
+  trunc_mean <- lambda / one_minus_p0
+  trunc_var <- (lambda + lambda^2 * (1 + theta)) / one_minus_p0 - trunc_mean^2
+  switch(type,
+    data = x,
+    raw = x - trunc_mean,
+    standardized = (x - trunc_mean) / sqrt(trunc_var),
+    dev = dev_gamma_pois_zt(x, lambda = lambda, theta = theta, res = TRUE),
+    chk_subset(x, c("data", "raw", "dev", "standardized"))
+  )
+}
+
 #' Log-Normal Residuals
 #'
 #' @inheritParams params
diff --git a/man/dev_gamma_pois_zi.Rd b/man/dev_gamma_pois_zi.Rd
index 790d700f..c67a9d00 100644
--- a/man/dev_gamma_pois_zi.Rd
+++ b/man/dev_gamma_pois_zi.Rd
@@ -29,4 +29,8 @@ Zero-Inflated Gamma-Poisson Deviances
 \examples{
 dev_gamma_pois_zi(c(1, 3, 4), 3, 2)
 }
+\seealso{
+Other dev_dist # make live when complete: 
+\code{\link{dev_gamma_pois_zt}()}
+}
 \concept{dev_dist # make live when complete}
diff --git a/man/dev_gamma_pois_zt.Rd b/man/dev_gamma_pois_zt.Rd
new file mode 100644
index 00000000..df87402b
--- /dev/null
+++ b/man/dev_gamma_pois_zt.Rd
@@ -0,0 +1,34 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/dev.R
+\name{dev_gamma_pois_zt}
+\alias{dev_gamma_pois_zt}
+\title{Zero-Truncated Gamma-Poisson Deviances}
+\usage{
+dev_gamma_pois_zt(x, lambda = 1, theta = 0, res = FALSE)
+}
+\arguments{
+\item{x}{A whole numeric vector of values greater than or equal to 1.}
+
+\item{lambda}{A non-negative numeric vector of means.}
+
+\item{theta}{A non-negative numeric vector of the dispersion for the mixture
+models (student, gamma-Poisson and beta-binomial).}
+
+\item{res}{A flag specifying whether to return the deviance residual as
+opposed to the deviance.}
+}
+\value{
+An numeric vector of the corresponding deviances or deviance residuals.
+}
+\description{
+Saturated log-likelihood is found numerically per observation since the
+truncated likelihood has no closed-form maximum.
+}
+\examples{
+dev_gamma_pois_zt(c(1, 3, 4), 3, 2)
+}
+\seealso{
+Other dev_dist # make live when complete: 
+\code{\link{dev_gamma_pois_zi}()}
+}
+\concept{dev_dist # make live when complete}
diff --git a/man/log_lik_bern.Rd b/man/log_lik_bern.Rd
index cefc8642..440e1440 100644
--- a/man/log_lik_bern.Rd
+++ b/man/log_lik_bern.Rd
@@ -30,6 +30,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_beta.Rd b/man/log_lik_beta.Rd
index 565d05dc..7be6aa73 100644
--- a/man/log_lik_beta.Rd
+++ b/man/log_lik_beta.Rd
@@ -31,6 +31,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_beta_binom.Rd b/man/log_lik_beta_binom.Rd
index 4fc365e5..3e2e91ae 100644
--- a/man/log_lik_beta_binom.Rd
+++ b/man/log_lik_beta_binom.Rd
@@ -45,6 +45,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_binom.Rd b/man/log_lik_binom.Rd
index 53369af5..863dd5b6 100644
--- a/man/log_lik_binom.Rd
+++ b/man/log_lik_binom.Rd
@@ -32,6 +32,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_exp.Rd b/man/log_lik_exp.Rd
index 2dbbd29f..95187fa0 100644
--- a/man/log_lik_exp.Rd
+++ b/man/log_lik_exp.Rd
@@ -29,6 +29,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_gamma.Rd b/man/log_lik_gamma.Rd
index ae073723..7e1c3b47 100644
--- a/man/log_lik_gamma.Rd
+++ b/man/log_lik_gamma.Rd
@@ -31,6 +31,7 @@ Other log_lik_dist:
 \code{\link{log_lik_exp}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_gamma_pois.Rd b/man/log_lik_gamma_pois.Rd
index 9041c389..17059b56 100644
--- a/man/log_lik_gamma_pois.Rd
+++ b/man/log_lik_gamma_pois.Rd
@@ -32,6 +32,7 @@ Other log_lik_dist:
 \code{\link{log_lik_exp}()},
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_gamma_pois_zi.Rd b/man/log_lik_gamma_pois_zi.Rd
index fed48ce0..145f3772 100644
--- a/man/log_lik_gamma_pois_zi.Rd
+++ b/man/log_lik_gamma_pois_zi.Rd
@@ -35,6 +35,7 @@ Other log_lik_dist:
 \code{\link{log_lik_exp}()},
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_gamma_pois_zt.Rd b/man/log_lik_gamma_pois_zt.Rd
new file mode 100644
index 00000000..cb9b6c2e
--- /dev/null
+++ b/man/log_lik_gamma_pois_zt.Rd
@@ -0,0 +1,45 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/log-lik.R
+\name{log_lik_gamma_pois_zt}
+\alias{log_lik_gamma_pois_zt}
+\title{Zero-Truncated Gamma-Poisson Log-Likelihood}
+\usage{
+log_lik_gamma_pois_zt(x, lambda = 1, theta = 0)
+}
+\arguments{
+\item{x}{A whole numeric vector of values greater than or equal to 1.}
+
+\item{lambda}{A non-negative numeric vector of means.}
+
+\item{theta}{A non-negative numeric vector of the dispersion for the mixture
+models (student, gamma-Poisson and beta-binomial).}
+}
+\value{
+An numeric vector of the corresponding log-likelihoods.
+}
+\description{
+Zero-Truncated Gamma-Poisson Log-Likelihood
+}
+\examples{
+log_lik_gamma_pois_zt(c(1, 3, 4), 3, 1)
+}
+\seealso{
+Other log_lik_dist: 
+\code{\link{log_lik_bern}()},
+\code{\link{log_lik_beta}()},
+\code{\link{log_lik_beta_binom}()},
+\code{\link{log_lik_binom}()},
+\code{\link{log_lik_exp}()},
+\code{\link{log_lik_gamma}()},
+\code{\link{log_lik_gamma_pois}()},
+\code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_lnorm}()},
+\code{\link{log_lik_neg_binom}()},
+\code{\link{log_lik_norm}()},
+\code{\link{log_lik_pois}()},
+\code{\link{log_lik_pois_zi}()},
+\code{\link{log_lik_skewnorm}()},
+\code{\link{log_lik_student}()},
+\code{\link{log_lik_unif}()}
+}
+\concept{log_lik_dist}
diff --git a/man/log_lik_lnorm.Rd b/man/log_lik_lnorm.Rd
index 7d7d3e02..515f5724 100644
--- a/man/log_lik_lnorm.Rd
+++ b/man/log_lik_lnorm.Rd
@@ -33,6 +33,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
 \code{\link{log_lik_pois}()},
diff --git a/man/log_lik_neg_binom.Rd b/man/log_lik_neg_binom.Rd
index 8d47937e..4b7f7adc 100644
--- a/man/log_lik_neg_binom.Rd
+++ b/man/log_lik_neg_binom.Rd
@@ -33,6 +33,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_norm}()},
 \code{\link{log_lik_pois}()},
diff --git a/man/log_lik_norm.Rd b/man/log_lik_norm.Rd
index 8d1b3c34..c48f3ca2 100644
--- a/man/log_lik_norm.Rd
+++ b/man/log_lik_norm.Rd
@@ -32,6 +32,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_pois}()},
diff --git a/man/log_lik_pois.Rd b/man/log_lik_pois.Rd
index 26e0de54..d56f178e 100644
--- a/man/log_lik_pois.Rd
+++ b/man/log_lik_pois.Rd
@@ -30,6 +30,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_pois_zi.Rd b/man/log_lik_pois_zi.Rd
index 8f378a9f..10e45c06 100644
--- a/man/log_lik_pois_zi.Rd
+++ b/man/log_lik_pois_zi.Rd
@@ -33,6 +33,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_skewnorm.Rd b/man/log_lik_skewnorm.Rd
index 93e60f2a..3a1e25e1 100644
--- a/man/log_lik_skewnorm.Rd
+++ b/man/log_lik_skewnorm.Rd
@@ -38,6 +38,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_student.Rd b/man/log_lik_student.Rd
index d392447c..1bb261ca 100644
--- a/man/log_lik_student.Rd
+++ b/man/log_lik_student.Rd
@@ -35,6 +35,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/log_lik_unif.Rd b/man/log_lik_unif.Rd
index a2996430..27da9ef6 100644
--- a/man/log_lik_unif.Rd
+++ b/man/log_lik_unif.Rd
@@ -32,6 +32,7 @@ Other log_lik_dist:
 \code{\link{log_lik_gamma}()},
 \code{\link{log_lik_gamma_pois}()},
 \code{\link{log_lik_gamma_pois_zi}()},
+\code{\link{log_lik_gamma_pois_zt}()},
 \code{\link{log_lik_lnorm}()},
 \code{\link{log_lik_neg_binom}()},
 \code{\link{log_lik_norm}()},
diff --git a/man/ran_bern.Rd b/man/ran_bern.Rd
index 2ccc2555..3be44ce3 100644
--- a/man/ran_bern.Rd
+++ b/man/ran_bern.Rd
@@ -29,6 +29,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_beta_binom.Rd b/man/ran_beta_binom.Rd
index bfca892e..e80beb49 100644
--- a/man/ran_beta_binom.Rd
+++ b/man/ran_beta_binom.Rd
@@ -42,6 +42,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_binom.Rd b/man/ran_binom.Rd
index 7084843e..78823fc0 100644
--- a/man/ran_binom.Rd
+++ b/man/ran_binom.Rd
@@ -31,6 +31,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_gamma.Rd b/man/ran_gamma.Rd
index 923a88fe..edba7369 100644
--- a/man/ran_gamma.Rd
+++ b/man/ran_gamma.Rd
@@ -30,6 +30,7 @@ Other ran_dist:
 \code{\link{ran_binom}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_gamma_pois.Rd b/man/ran_gamma_pois.Rd
index 50e0c60b..57d39ef2 100644
--- a/man/ran_gamma_pois.Rd
+++ b/man/ran_gamma_pois.Rd
@@ -31,6 +31,7 @@ Other ran_dist:
 \code{\link{ran_binom}()},
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_gamma_pois_zi.Rd b/man/ran_gamma_pois_zi.Rd
index 5a70d40c..bb574037 100644
--- a/man/ran_gamma_pois_zi.Rd
+++ b/man/ran_gamma_pois_zi.Rd
@@ -34,6 +34,7 @@ Other ran_dist:
 \code{\link{ran_binom}()},
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_gamma_pois_zt.Rd b/man/ran_gamma_pois_zt.Rd
new file mode 100644
index 00000000..fb2a1064
--- /dev/null
+++ b/man/ran_gamma_pois_zt.Rd
@@ -0,0 +1,43 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/ran.R
+\name{ran_gamma_pois_zt}
+\alias{ran_gamma_pois_zt}
+\title{Zero-Truncated Gamma-Poisson Random Samples}
+\usage{
+ran_gamma_pois_zt(n = 1, lambda = 1, theta = 0)
+}
+\arguments{
+\item{n}{A non-negative whole number of the number of random samples to
+generate.}
+
+\item{lambda}{A non-negative numeric vector of means.}
+
+\item{theta}{A non-negative numeric vector of the dispersion for the mixture
+models (student, gamma-Poisson and beta-binomial).}
+}
+\value{
+A numeric vector of the random samples.
+}
+\description{
+Drawn via rejection sampling so all returned values are at least 1.
+}
+\examples{
+ran_gamma_pois_zt(10, lambda = 3, theta = 1)
+}
+\seealso{
+Other ran_dist: 
+\code{\link{ran_bern}()},
+\code{\link{ran_beta_binom}()},
+\code{\link{ran_binom}()},
+\code{\link{ran_gamma}()},
+\code{\link{ran_gamma_pois}()},
+\code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_lnorm}()},
+\code{\link{ran_neg_binom}()},
+\code{\link{ran_norm}()},
+\code{\link{ran_pois}()},
+\code{\link{ran_pois_zi}()},
+\code{\link{ran_skewnorm}()},
+\code{\link{ran_student}()}
+}
+\concept{ran_dist}
diff --git a/man/ran_lnorm.Rd b/man/ran_lnorm.Rd
index 03ac9612..d1cef892 100644
--- a/man/ran_lnorm.Rd
+++ b/man/ran_lnorm.Rd
@@ -32,6 +32,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
 \code{\link{ran_pois}()},
diff --git a/man/ran_neg_binom.Rd b/man/ran_neg_binom.Rd
index 19567ec2..062c1750 100644
--- a/man/ran_neg_binom.Rd
+++ b/man/ran_neg_binom.Rd
@@ -32,6 +32,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_norm}()},
 \code{\link{ran_pois}()},
diff --git a/man/ran_norm.Rd b/man/ran_norm.Rd
index 4bc7ce72..8ab610d8 100644
--- a/man/ran_norm.Rd
+++ b/man/ran_norm.Rd
@@ -31,6 +31,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_pois}()},
diff --git a/man/ran_pois.Rd b/man/ran_pois.Rd
index 92c70b62..716bbb10 100644
--- a/man/ran_pois.Rd
+++ b/man/ran_pois.Rd
@@ -29,6 +29,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_pois_zi.Rd b/man/ran_pois_zi.Rd
index cb707984..de49883a 100644
--- a/man/ran_pois_zi.Rd
+++ b/man/ran_pois_zi.Rd
@@ -32,6 +32,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_skewnorm.Rd b/man/ran_skewnorm.Rd
index 805c4d11..7d616456 100644
--- a/man/ran_skewnorm.Rd
+++ b/man/ran_skewnorm.Rd
@@ -37,6 +37,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/ran_student.Rd b/man/ran_student.Rd
index ffbdb0bc..4d5e8f66 100644
--- a/man/ran_student.Rd
+++ b/man/ran_student.Rd
@@ -34,6 +34,7 @@ Other ran_dist:
 \code{\link{ran_gamma}()},
 \code{\link{ran_gamma_pois}()},
 \code{\link{ran_gamma_pois_zi}()},
+\code{\link{ran_gamma_pois_zt}()},
 \code{\link{ran_lnorm}()},
 \code{\link{ran_neg_binom}()},
 \code{\link{ran_norm}()},
diff --git a/man/res_bern.Rd b/man/res_bern.Rd
index 13cf16c4..bff0965d 100644
--- a/man/res_bern.Rd
+++ b/man/res_bern.Rd
@@ -33,6 +33,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_beta_binom.Rd b/man/res_beta_binom.Rd
index b7fd0675..621cdf05 100644
--- a/man/res_beta_binom.Rd
+++ b/man/res_beta_binom.Rd
@@ -53,6 +53,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_binom.Rd b/man/res_binom.Rd
index ad2fc8e1..ec20d03c 100644
--- a/man/res_binom.Rd
+++ b/man/res_binom.Rd
@@ -35,6 +35,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_gamma.Rd b/man/res_gamma.Rd
index 6b98bcfd..9f1bd8cb 100644
--- a/man/res_gamma.Rd
+++ b/man/res_gamma.Rd
@@ -34,6 +34,7 @@ Other res_dist:
 \code{\link{res_binom}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_gamma_pois.Rd b/man/res_gamma_pois.Rd
index c8d276cd..f36e9b03 100644
--- a/man/res_gamma_pois.Rd
+++ b/man/res_gamma_pois.Rd
@@ -35,6 +35,7 @@ Other res_dist:
 \code{\link{res_binom}()},
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_gamma_pois_zi.Rd b/man/res_gamma_pois_zi.Rd
index 69aa04c0..21982b30 100644
--- a/man/res_gamma_pois_zi.Rd
+++ b/man/res_gamma_pois_zi.Rd
@@ -44,6 +44,7 @@ Other res_dist:
 \code{\link{res_binom}()},
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_gamma_pois_zt.Rd b/man/res_gamma_pois_zt.Rd
new file mode 100644
index 00000000..ec3c4b8b
--- /dev/null
+++ b/man/res_gamma_pois_zt.Rd
@@ -0,0 +1,47 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/res.R
+\name{res_gamma_pois_zt}
+\alias{res_gamma_pois_zt}
+\title{Zero-Truncated Gamma-Poisson Residuals}
+\usage{
+res_gamma_pois_zt(x, lambda = 1, theta = 0, type = "dev", simulate = FALSE)
+}
+\arguments{
+\item{x}{A whole numeric vector of values greater than or equal to 1.}
+
+\item{lambda}{A non-negative numeric vector of means.}
+
+\item{theta}{A non-negative numeric vector of the dispersion for the mixture
+models (student, gamma-Poisson and beta-binomial).}
+
+\item{type}{A string of the residual type. 'raw' for raw residuals 'dev' for
+deviance residuals and 'data' for the data.}
+
+\item{simulate}{A flag specifying whether to simulate residuals.}
+}
+\value{
+An numeric vector of the corresponding residuals.
+}
+\description{
+Centred on the truncated mean and standardised by the truncated variance.
+}
+\examples{
+res_gamma_pois_zt(c(1, 2, 5), 2, 1)
+}
+\seealso{
+Other res_dist: 
+\code{\link{res_bern}()},
+\code{\link{res_beta_binom}()},
+\code{\link{res_binom}()},
+\code{\link{res_gamma}()},
+\code{\link{res_gamma_pois}()},
+\code{\link{res_gamma_pois_zi}()},
+\code{\link{res_lnorm}()},
+\code{\link{res_neg_binom}()},
+\code{\link{res_norm}()},
+\code{\link{res_pois}()},
+\code{\link{res_pois_zi}()},
+\code{\link{res_skewnorm}()},
+\code{\link{res_student}()}
+}
+\concept{res_dist}
diff --git a/man/res_lnorm.Rd b/man/res_lnorm.Rd
index 948bbed0..bb4d559b 100644
--- a/man/res_lnorm.Rd
+++ b/man/res_lnorm.Rd
@@ -36,6 +36,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
 \code{\link{res_pois}()},
diff --git a/man/res_neg_binom.Rd b/man/res_neg_binom.Rd
index c8680a53..6c2e8412 100644
--- a/man/res_neg_binom.Rd
+++ b/man/res_neg_binom.Rd
@@ -36,6 +36,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_norm}()},
 \code{\link{res_pois}()},
diff --git a/man/res_norm.Rd b/man/res_norm.Rd
index 0e964dd3..1ac62259 100644
--- a/man/res_norm.Rd
+++ b/man/res_norm.Rd
@@ -35,6 +35,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_pois}()},
diff --git a/man/res_pois.Rd b/man/res_pois.Rd
index 68e0ff4f..7d490785 100644
--- a/man/res_pois.Rd
+++ b/man/res_pois.Rd
@@ -33,6 +33,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_pois_zi.Rd b/man/res_pois_zi.Rd
index 43b3df93..fb42947d 100644
--- a/man/res_pois_zi.Rd
+++ b/man/res_pois_zi.Rd
@@ -35,6 +35,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_skewnorm.Rd b/man/res_skewnorm.Rd
index 0d2c53c5..765e35ec 100644
--- a/man/res_skewnorm.Rd
+++ b/man/res_skewnorm.Rd
@@ -39,6 +39,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/man/res_student.Rd b/man/res_student.Rd
index 52d7d783..d30a4c71 100644
--- a/man/res_student.Rd
+++ b/man/res_student.Rd
@@ -38,6 +38,7 @@ Other res_dist:
 \code{\link{res_gamma}()},
 \code{\link{res_gamma_pois}()},
 \code{\link{res_gamma_pois_zi}()},
+\code{\link{res_gamma_pois_zt}()},
 \code{\link{res_lnorm}()},
 \code{\link{res_neg_binom}()},
 \code{\link{res_norm}()},
diff --git a/tests/testthat/test-dev.R b/tests/testthat/test-dev.R
index 6bd2a5e0..2a620eff 100644
--- a/tests/testthat/test-dev.R
+++ b/tests/testthat/test-dev.R
@@ -316,6 +316,38 @@ test_that("gamma_pois_zi vectorized", {
   expect_equal(dev_gamma_pois_zi(0:3, 3:0, 0:3, seq(0, 1, length.out = 4)), c(6, 1.0464962875291, 2.41568518074605, Inf))
 })
 
+test_that("gamma_pois_zt missing values", {
+  expect_identical(dev_gamma_pois_zt(logical(0), integer(0), numeric(0)), numeric(0))
+  expect_identical(dev_gamma_pois_zt(NA, 1, 1), NA_real_)
+  expect_identical(dev_gamma_pois_zt(1, NA, 1), NA_real_)
+  expect_identical(dev_gamma_pois_zt(1, 1, NA), NA_real_)
+})
+
+test_that("gamma_pois_zt known values", {
+  expect_equal(dev_gamma_pois_zt(c(1, 3, 4), 3, 2),
+               c(2.69098973, 0.19520565, 0.03152929),
+               tolerance = 1e-6)
+  expect_equal(dev_gamma_pois_zt(3, 3), 0.009522421, tolerance = 1e-6)
+})
+
+test_that("gamma_pois_zt deviance is non-negative", {
+  expect_true(all(dev_gamma_pois_zt(1:20, 5, 1) >= 0))
+  expect_true(all(dev_gamma_pois_zt(1:20, 10, 0.5) >= 0))
+  expect_true(all(dev_gamma_pois_zt(1:20, 1, 2) >= 0))
+})
+
+test_that("gamma_pois_zt deviance residuals", {
+  # Residuals signed by sign(x - trunc_mean) and scaled by sqrt(dev).
+  expect_equal(dev_gamma_pois_zt(c(1, 2, 5), 2, 1, res = TRUE),
+               c(-1.4823038, -0.4853515, 0.6610002),
+               tolerance = 1e-6)
+  # Sign follows sign(x - trunc_mean). For lambda = 2, theta = 1,
+  # trunc_mean = 2 / (1 - 1/3) = 3.
+  trunc_mean_at_2_1 <- 2 / (1 - dnbinom(0, mu = 2, size = 1))
+  expect_equal(sign(dev_gamma_pois_zt(c(1, 5), 2, 1, res = TRUE)),
+               sign(c(1, 5) - trunc_mean_at_2_1))
+})
+
 test_that("gamma_pois_zi vectorized missing values", {
   expect_equal(dev_gamma_pois_zi(c(NA, 1), 0:1, 0:1, 0:1), c(NA, Inf))
   expect_equal(dev_gamma_pois_zi(c(0, NA), 0:1, 0:1, 0:1), c(0, NA))
diff --git a/tests/testthat/test-log-lik.R b/tests/testthat/test-log-lik.R
index aca1621c..fd354232 100644
--- a/tests/testthat/test-log-lik.R
+++ b/tests/testthat/test-log-lik.R
@@ -113,6 +113,35 @@ test_that("gamma_pois_zi vectorized", {
   expect_equal(log_lik_gamma_pois_zi(0:3, 3:0, 0:3, seq(0, 1, length.out = 4)), c(-3, -1.90954250488444, -3.43967790223022, -Inf))
 })
 
+test_that("gamma_pois_zt missing values", {
+  expect_identical(log_lik_gamma_pois_zt(numeric(0), numeric(0), numeric(0)), numeric(0))
+  expect_identical(log_lik_gamma_pois_zt(NA, 1, 1), NA_real_)
+  expect_identical(log_lik_gamma_pois_zt(1, NA, 1), NA_real_)
+  expect_identical(log_lik_gamma_pois_zt(1, 1, NA), NA_real_)
+})
+
+test_that("gamma_pois_zt known values", {
+  expect_equal(log_lik_gamma_pois_zt(1, 2), -1.1614393615712)
+  expect_equal(log_lik_gamma_pois_zt(2, 2), -1.1614393615712)
+  expect_equal(log_lik_gamma_pois_zt(1, 2, 0.5), -1.09861228866811)
+  expect_equal(log_lik_gamma_pois_zt(c(1, 3, 4), 3, 1),
+               c(-1.38629436111989, -1.96165850602345, -2.24934057847523))
+})
+
+test_that("gamma_pois_zt vectorized", {
+  expect_equal(log_lik_gamma_pois_zt(1:3, 2, 0),
+               c(-1.1614393615712, -1.1614393615712, -1.56690446967936))
+})
+
+test_that("gamma_pois_zt matches truncated NB conditional", {
+  # log L_zt(x; mu, theta) = log NB(x; mu, theta) - log(1 - P(0; mu, theta))
+  expect_equal(
+    log_lik_gamma_pois_zt(2, 3, 1),
+    dnbinom(2, mu = 3, size = 1, log = TRUE) -
+      log1p(-dnbinom(0, mu = 3, size = 1))
+  )
+})
+
 test_that("gamma missing values", {
   expect_identical(log_lik_gamma(NA), NA_real_)
   expect_identical(log_lik_gamma(1, NA), NA_real_)
diff --git a/tests/testthat/test-ran.R b/tests/testthat/test-ran.R
index 0c375d75..185c0b6e 100644
--- a/tests/testthat/test-ran.R
+++ b/tests/testthat/test-ran.R
@@ -146,6 +146,39 @@ test_that("ran_gamma_pois_zi", {
   expect_identical(ran_gamma_pois_zi(1, c(0.1, 100), theta = 1, prob = 0.5), 0L)
 })
 
+test_that("ran_gamma_pois_zt", {
+  expect_error(ran_gamma_pois_zt(NA_integer_))
+  expect_error(ran_gamma_pois_zt(integer(0)))
+  expect_identical(ran_gamma_pois_zt(0L), integer(0))
+  set.seed(101)
+  expect_identical(ran_gamma_pois_zt(), 1L)
+  expect_identical(ran_gamma_pois_zt(2), c(3L, 2L))
+  expect_identical(ran_gamma_pois_zt(2, 10), c(7L, 7L))
+  expect_identical(ran_gamma_pois_zt(2, c(0.1, 100)), c(1L, 95L))
+  set.seed(101)
+  expect_identical(ran_gamma_pois_zt(2, theta = 10), c(2L, 1L))
+  expect_identical(ran_gamma_pois_zt(2, 10, theta = 10), c(7L, 13L))
+  expect_identical(ran_gamma_pois_zt(2, c(0.1, 100), theta = 1), c(1L, 12L))
+})
+
+test_that("ran_gamma_pois_zt always >= 1", {
+  set.seed(42)
+  # Even with very small lambda where most untruncated draws would be 0,
+  # rejection sampling guarantees all returned values are >= 1.
+  y <- ran_gamma_pois_zt(2000, lambda = 0.5, theta = 1)
+  expect_true(all(y >= 1))
+  expect_length(y, 2000)
+})
+
+test_that("ran_gamma_pois_zt mean approximates truncated mean", {
+  set.seed(42)
+  lambda <- 5
+  theta <- 0.5
+  y <- ran_gamma_pois_zt(20000, lambda = lambda, theta = theta)
+  expected <- lambda / (1 - dnbinom(0, mu = lambda, size = 1 / theta))
+  expect_equal(mean(y), expected, tolerance = 0.05)
+})
+
 test_that("ran_gamma", {
   expect_error(ran_gamma(NA_integer_))
   expect_error(ran_gamma(integer(0)))
diff --git a/tests/testthat/test-res.R b/tests/testthat/test-res.R
index 0bbf882c..32ad2464 100644
--- a/tests/testthat/test-res.R
+++ b/tests/testthat/test-res.R
@@ -380,6 +380,52 @@ test_that("res_gamma_pois_zi", {
   expect_equal(sd(res), 0.860406154019735)
 })
 
+test_that("res_gamma_pois_zt", {
+  expect_identical(res_gamma_pois_zt(integer(0), integer(0), integer(0)), numeric(0))
+  expect_identical(res_gamma_pois_zt(NA, 1, 1), NA_real_)
+  expect_identical(res_gamma_pois_zt(1, NA, 1), NA_real_)
+  expect_identical(res_gamma_pois_zt(1, 1, NA), NA_real_)
+  expect_error(res_gamma_pois_zt(1, 1, 1, type = "unknown"))
+
+  # type = "data"
+  expect_identical(res_gamma_pois_zt(1:3, 2, 1, type = "data"), 1:3)
+
+  # type = "raw" — residual is x - truncated mean
+  # truncated mean for lambda = 2, theta = 1 is 2 / (1 - 1/3) = 3
+  expect_equal(res_gamma_pois_zt(c(1, 3, 5), 2, 1, type = "raw"), c(-2, 0, 2))
+  # When theta -> 0, truncated mean approaches lambda for moderate lambda
+  expect_equal(
+    res_gamma_pois_zt(c(1, 10, 20), 10, 0, type = "raw"),
+    c(1, 10, 20) - 10 / (1 - exp(-10))
+  )
+
+  # type = "standardized" — residual is (x - trunc_mean) / sqrt(trunc_var)
+  # For lambda = 3, theta = 1: trunc_mean = 4, trunc_var = 12
+  expect_equal(
+    res_gamma_pois_zt(c(1, 3, 4), 3, 1, type = "standardized"),
+    (c(1, 3, 4) - 4) / sqrt(12)
+  )
+
+  # type = "dev" — saturated MLE found numerically per observation,
+  # signed by sign(x - trunc_mean)
+  expect_equal(
+    res_gamma_pois_zt(c(1, 2, 5), 2, 1),
+    c(-1.4823038, -0.4853515, 0.6610002),
+    tolerance = 1e-6
+  )
+
+  # simulate = TRUE replaces x with random draws from ZT distribution
+  set.seed(101)
+  expect_true(all(res_gamma_pois_zt(1:5, 2, 1, simulate = TRUE, type = "data") >= 1))
+
+  # Standardised residuals on simulated data approximate N(0, 1)
+  set.seed(101)
+  res <- res_gamma_pois_zt(rep(2, 10000), 2, 1, simulate = TRUE,
+                           type = "standardized")
+  expect_equal(mean(res), 0, tolerance = 0.05)
+  expect_equal(sd(res), 1, tolerance = 0.05)
+})
+
 test_that("res_gamma", {
   expect_identical(res_gamma(integer(0), integer(0), integer(0)), numeric(0))
   expect_identical(res_gamma(1, 1, 1), 0)