DelayedExponential: Delayed Exponential Distribution

In incubate: Parametric Time-to-Event Analysis with Variable Incubation Phases

Delayed Exponential Distribution

Description

Density, distribution function, quantile function, random generation and restricted mean survival time function for the delayed exponential distribution. There is an initial delay phase (parameter delay1) where no events occur. After that, rate1 applies. Optionally, a second phase is possible where the hazard rate might change (parameters delay2 and rate2).

Usage

dexp_delayed(
  x,
  delay1 = 0,
  rate1 = 1,
  delay2 = NULL,
  rate2 = NULL,
  delay = delay1,
  rate = rate1,
  log = FALSE
)

pexp_delayed(
  q,
  delay1 = 0,
  rate1 = 1,
  delay2 = NULL,
  rate2 = NULL,
  delay = delay1,
  rate = rate1,
  ...
)

qexp_delayed(
  p,
  delay1 = 0,
  rate1 = 1,
  delay2 = NULL,
  rate2 = NULL,
  delay = delay1,
  rate = rate1,
  lower.tail = TRUE,
  log.p = FALSE
)

rexp_delayed(
  n,
  delay1 = 0,
  rate1 = 1,
  delay2 = NULL,
  rate2 = NULL,
  delay = delay1,
  rate = rate1
)

mexp_delayed(
  t = +Inf,
  delay1 = 0,
  rate1 = 1,
  delay2 = NULL,
  rate2 = NULL,
  delay = delay1,
  rate = rate1
)

Arguments

x	A numeric vector of values for which to get the density.
delay1	numeric. The first delay, must be non-negative.
rate1	numeric. The event rate, must be non-negative.
delay2	numeric. The second delay, must be non-negative.
rate2	numeric. The second event rate, must be non-negative.
delay	numeric. Alias for first delay.
rate	numeric. Alias for first rate.
log	logical. Return value on log-scale?
q	A numeric vector of quantile values.
...	further arguments are passed on to the underlying non-delayed function, e.g., ⁠lower.tail=⁠ to stats::pexp()
p	A numeric vector of probabilities.
lower.tail	logical. Give cumulative probability of lower tail?
log.p	logical. P-value on log-sclae?
n	integer. Number of random observations requested.
t	A numeric vector of times that restrict the mean survival. Default is +Inf, i.e., the unrestricted mean survival time.

Details

Additional arguments are forwarded via ... to the underlying functions of the exponential distribution in the stats-package. If only a single initial delay phase is there, the numerical arguments other than n are recycled to the length of the result (as with the exponential distribution in stats). With two phases, the arguments are not recycled. Only the first element of delays and rates are used as it otherwise becomes ambiguous which delay and rate parameter apply for observations in different phases. Generally, only the first elements of the logical arguments are used.

Value

Functions pertaining to the delayed exponential distribution:

• dexp_delayed gives the density

• pexp_delayed gives the distribution function

• qexp_delayed gives the quantile function

• rexp_delayed generates a pseudo-random sample

• mexp_delayed gives the restricted mean survival time

The length of the result is determined by n for rexp_delayed, and is the maximum of the lengths of the numerical arguments for the other functions, R's recycling rules apply when only single initial delay phase is used.

See Also

stats::Exponential

incubate documentation built on Sept. 11, 2024, 6:50 p.m.