dprimarycensored: Compute the primary event censored PMF for delays

In primarycensored: Primary Event Censored Distributions

Compute the primary event censored PMF for delays

Description

This function computes the primary event censored probability mass function (PMF) for a given set of quantiles. It adjusts the PMF of the primary event distribution by accounting for the delay distribution and potential truncation at a maximum delay (D) and minimum delay (L). The function allows for custom primary event distributions and delay distributions.

Usage

dprimarycensored(
  x,
  pdist,
  pwindow = 1,
  swindow = 1,
  L = -Inf,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  log = FALSE,
  ...
)

dpcens(
  x,
  pdist,
  pwindow = 1,
  swindow = 1,
  L = -Inf,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  log = FALSE,
  ...
)

Arguments

x	Vector of quantiles
pdist	Distribution function (CDF). The package can identify base R distributions for potential analytical solutions. For non-base R functions, users can apply add_name_attribute() to yield properly tagged functions if they wish to leverage the analytical solutions.
pwindow	Primary event window
swindow	Secondary event window (default: 1)
L	Minimum delay (lower truncation point). Defaults to -Inf, meaning no left truncation. For any finite value of L the distribution is left-truncated at L.
D	Maximum delay (upper truncation point). If finite, the distribution is truncated at D. If set to Inf, no upper truncation is applied. Defaults to Inf.
dprimary	Function to generate the probability density function (PDF) of primary event times. This function should take a value x and a pwindow parameter, and return a probability density. It should be normalized to integrate to 1 over [0, pwindow]. Defaults to a uniform distribution over [0, pwindow]. Users can provide custom functions or use helper functions like dexpgrowth for an exponential growth distribution. See pcd_primary_distributions() for examples. The package can identify base R distributions for potential analytical solutions. For non-base R functions, users can apply add_name_attribute() to yield properly tagged functions if they wish to leverage analytical solutions.
dprimary_args	List of additional arguments to be passed to dprimary. For example, when using dexpgrowth, you would pass list(min = 0, max = pwindow, r = 0.2) to set the minimum, maximum, and rate parameters
log	Logical; if TRUE, probabilities p are given as log(p)
...	Additional arguments to be passed to the distribution function

Details

The primary event censored PMF is computed by taking the difference of the primary event censored cumulative distribution function (CDF) at two points, d + \text{swindow} and d. The primary event censored PMF, f_{\text{cens}}(d), is given by:

f_{\text{cens}}(d) = F_{\text{cens}}(d + \text{swindow}) - F_{\text{cens}}(d)

where F_{\text{cens}} is the primary event censored CDF.

The function first computes the CDFs for all unique points (including both d and d + \text{swindow}) using pprimarycensored(). It then creates a lookup table for these CDFs to efficiently calculate the PMF for each input value. For delays less than L, the function returns 0.

The PMF is normalised to ensure it sums to 1 over the range [L, D\). This normalization uses:

f_{\text{cens,norm}}(d) = \frac{f_{\text{cens}}(d)}{ F_{\text{cens}}(D) - F_{\text{cens}}(L)}

where f_{\text{cens,norm}}(d) is the normalized PMF. For the explanation and mathematical details of the CDF, refer to the documentation of pprimarycensored().

Value

Vector of primary event censored PMFs, normalized over [L, D] if truncation is applied

See Also

Primary event censored distribution functions pprimarycensored(), qprimarycensored(), rprimarycensored()

Examples

# Example: Weibull distribution with uniform primary events
dprimarycensored(c(0.1, 0.5, 1), pweibull, shape = 1.5, scale = 2.0)

# Example: Weibull distribution with exponential growth primary events
dprimarycensored(
  c(0.1, 0.5, 1), pweibull,
  dprimary = dexpgrowth,
  dprimary_args = list(r = 0.2), shape = 1.5, scale = 2.0
)

# Example: Left-truncated distribution (e.g., for generation intervals)
dprimarycensored(1:9, pweibull, L = 1, D = 10, shape = 1.5, scale = 2.0)

primarycensored documentation built on June 15, 2026, 5:06 p.m.