diff --git a/NEWS.md b/NEWS.md
index d1bbfbb..0c93319 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -13,6 +13,7 @@ This is the development version of `primarycensoreddist` and is not yet ready fo
 
 * Simplified the "Analytic solutions" vignette by removing verbose derivation details.
 * Added links between vignettes to make it easier to navigate the documentation.
+* Added explicit usage of `pdist`, `dprimary`, `rdist`, and `rprimary` arguments in the getting started vignette to make it easier to link to mathematical details.
 
 # primarycensoreddist 0.5.0
 
diff --git a/vignettes/primarycensoreddist.Rmd b/vignettes/primarycensoreddist.Rmd
index bced166..a2ca97a 100644
--- a/vignettes/primarycensoreddist.Rmd
+++ b/vignettes/primarycensoreddist.Rmd
@@ -82,15 +82,17 @@ pwindow <- 1
 
 # Random samples without secondary censoring
 samples <- rprimarycensoreddist(
-  n, rlnorm,
-  meanlog = meanlog, sdlog = sdlog,
-  pwindow = pwindow, swindow = 0, D = obs_time
+  n,
+  rdist = rlnorm, rprimary = runif,
+  pwindow = pwindow, swindow = 0, D = obs_time,
+  meanlog = meanlog, sdlog = sdlog
 )
 # Random samples with secondary censoring
 samples_sc <- rprimarycensoreddist(
-  n, rlnorm,
-  meanlog = meanlog, sdlog = sdlog,
-  pwindow = pwindow, swindow = 1, D = obs_time
+  n,
+  rdist = rlnorm, rprimary = runif,
+  pwindow = pwindow, swindow = 1, D = obs_time,
+  meanlog = meanlog, sdlog = sdlog
 )
 # Calculate the PMF for the samples with secondary censoring
 samples_sc_pmf <- data.frame(
@@ -172,9 +174,9 @@ Let's compare the empirical CDF of our samples without secondary censoring to th
 empirical_cdf <- ecdf(samples)
 theoretical_cdf <- pprimarycensoreddist(
   seq(0, obs_time, length.out = 100),
-  plnorm,
-  meanlog = meanlog, sdlog = sdlog,
-  pwindow = pwindow, D = obs_time
+  pdist = plnorm, dprimary = dunif,
+  pwindow = pwindow, D = obs_time,
+  meanlog = meanlog, sdlog = sdlog
 )
 
 # Create a data frame for plotting
@@ -226,9 +228,9 @@ Let's compare the empirical PMF of our samples with secondary censoring to the t
 # Calculate the theoretical PMF using dprimarycensoreddist
 theoretical_pmf <- dprimarycensoreddist(
   0:(obs_time - 1),
-  plnorm,
-  meanlog = meanlog, sdlog = sdlog,
-  pwindow = pwindow, swindow = 1, D = obs_time
+  pdist = plnorm, dprimary = dunif,
+  pwindow = pwindow, swindow = 1, D = obs_time,
+  meanlog = meanlog, sdlog = sdlog
 )
 
 pmf_df <- data.frame(