Method for generalised gamma delay with uniform primary

Analytical solution for the generalised gamma distribution in the Stacy parameterisation used by flexsurv::pgengamma.orig(), with parameters shape, scale and k. The delay CDF is \(F_T(t) = P(k, (t / \theta)^a)\) with \(P\) the regularised lower incomplete gamma function, \(a\) the shape and \(\theta\) the scale. The mean is \(E[T] = \theta \Gamma(k + 1/a) / \Gamma(k)\) and the partial expectation distribution is \(\tilde F_T(t) = P(k + 1/a, (t / \theta)^a)\), so the solution generalises the gamma (shape = 1) and Weibull (k = 1) cases. See vignette("analytic-solutions") for the derivation.

Usage

# S3 method for class 'pcens_pgengamma.orig_dunif'
pcens_cdf(object, q, pwindow, use_numeric = FALSE)

Arguments

object

A primarycensored object as created by new_pcens().

q

Vector of quantiles

pwindow

Primary event window

use_numeric

Logical, if TRUE forces use of numeric integration even for distributions with analytical solutions. This is primarily useful for testing purposes or for settings where the analytical solution breaks down.

Value

Vector of computed primary event censored CDFs

See also

Low level primary event censored distribution objects and methods new_pcens(), pcens_cdf(), pcens_cdf.default(), pcens_cdf.pcens_pdiscretehazard(), pcens_cdf.pcens_pdiscretestep(), pcens_cdf.pcens_pgamma_dunif(), pcens_cdf.pcens_pgengamma_dunif(), pcens_cdf.pcens_plnorm_dunif(), pcens_cdf.pcens_pweibull_dunif(), pcens_quantile(), pcens_quantile.default()

Examples

pcens_obj <- new_pcens(
  pdist = flexsurv::pgengamma.orig,
  dprimary = dunif,
  dprimary_args = list(min = 0, max = 1),
  shape = 1.5,
  scale = 2,
  k = 0.8
)
#> Warning: The `dprimary_args` argument of `new_pcens()` is deprecated as of
#> primarycensored 1.6.0.
#> ℹ Please use the `primary_args` argument instead.
pcens_cdf(pcens_obj, q = c(1, 4, 8), pwindow = 1)
#> [1] 0.1940835 0.9298869 0.9995685