Compute the primary event censored CDF for delays

This function computes the primary event censored cumulative distribution function (CDF) for a given set of quantiles. It adjusts the CDF 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

pprimarycensored(
  q,
  pdist,
  pwindow = 1,
  L = -Inf,
  D = Inf,
  dprimary = dunif,
  primary_args = NULL,
  pprimary = NULL,
  dprimary_args = NULL,
  ...
)

ppcens(
  q,
  pdist,
  pwindow = 1,
  L = -Inf,
  D = Inf,
  dprimary = dunif,
  primary_args = NULL,
  pprimary = NULL,
  dprimary_args = NULL,
  ...
)

Arguments

q: 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
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.
primary_args: List of additional arguments to be passed to dprimary (and the matching primary CDF). For example, when using dexpgrowth, you would pass list(min = 0, max = pwindow, r = 0.2) to set the minimum, maximum, and rate parameters. Replaces the deprecated dprimary_args; defaults to NULL.
pprimary: Optional CDF for the primary event distribution. May be a function or a character string naming a primary distribution in pcd_primary_distributions. Defaults to NULL, in which case the primary CDF is looked up automatically from the registry using the "name" attribute of dprimary. When both dprimary and pprimary carry a "name" attribute (or are base R functions whose name can be inferred), the two names must agree on everything other than the leading d/p prefix; mismatches such as dunif + pexpgrowth raise an error. Supplying pprimary explicitly is mainly useful when using a custom primary distribution whose CDF is not in the registry.
dprimary_args: [Deprecated] Use primary_args instead.
...: Additional arguments to be passed to pdist

Value

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

Details

The primary event censored CDF is computed by integrating the product of the delay distribution function (CDF) and the primary event distribution function (PDF) over the primary event window. The integration is adjusted for truncation if specified.

The primary event censored CDF, $F_{\text{cens}}(q)$, is given by: $$ F_{\text{cens}}(q) = \int_{0}^{pwindow} F(q - p) \cdot f_{\text{primary}}(p) \, dp $$ where $F$ is the CDF of the delay distribution, $f_{\text{primary}}$ is the PDF of the primary event times, and $pwindow$ is the primary event window.

If truncation is applied (finite D or finite L), the CDF is normalized: $$ F_{\text{cens,norm}}(q) = \frac{F_{\text{cens}}(q) - F_{\text{cens}}(L)}{ F_{\text{cens}}(D) - F_{\text{cens}}(L)} $$ where $F_{\text{cens,norm}}(q)$ is the normalized CDF. For values $q \leq L$, the function returns 0; for values $q \geq D$, it returns 1.

This function creates a primarycensored object using new_pcens() and then computes the primary event censored CDF using pcens_cdf(). This abstraction allows for automatic use of analytical solutions when available, while seamlessly falling back to numerical integration when necessary.

See methods(pcens_cdf) for which combinations have analytical solutions implemented.

Examples

# Example: Lognormal distribution with uniform primary events
pprimarycensored(c(0.1, 0.5, 1), plnorm, meanlog = 0, sdlog = 1)
#> [1] 0.0002753888 0.0475094632 0.2384217081

# Example: Lognormal distribution with exponential growth primary events
pprimarycensored(
  c(0.1, 0.5, 1), plnorm,
  dprimary = dexpgrowth,
  primary_args = list(r = 0.2), meanlog = 0, sdlog = 1
)
#> [1] 0.0002496934 0.0440815583 0.2290795695

# Example: Left-truncated distribution (e.g., for generation intervals)
pprimarycensored(
  c(1, 2, 3), plnorm,
  L = 1, D = 10,
  meanlog = 0, sdlog = 1
)
#> [1] 0.0000000 0.5461907 0.7719056

Usage

Arguments

Value

Details

See also

Examples