DelayedWeibull: Delayed Weibull Distribution

Description

Density, distribution function, quantile function and random generation for the delayed Weibull distribution. Besides the additional parameter delay, the other two Weibull-parameters are in principle retained as in R's stats-package:

shape
scale (as inverse of rate)

Usage

dweib_delayed(
  x,
  delay1,
  shape1,
  scale1 = 1,
  delay2 = NULL,
  shape2 = NULL,
  scale2 = 1,
  delay = delay1,
  shape = shape1,
  scale = scale1,
  log = FALSE
)
pweib_delayed(
  q,
  delay1,
  shape1,
  scale1 = 1,
  delay2 = NULL,
  shape2 = NULL,
  scale2 = 1,
  delay = delay1,
  shape = shape1,
  scale = scale1,
  lower.tail = TRUE,
  log.p = FALSE
)
qweib_delayed(
  p,
  delay1,
  shape1,
  scale1 = 1,
  delay2 = NULL,
  shape2 = NULL,
  scale2 = 1,
  delay = delay1,
  shape = shape1,
  scale = scale1,
  lower.tail = TRUE,
  log.p = FALSE
)
rweib_delayed(
  n,
  delay1,
  shape1,
  scale1 = 1,
  delay2 = NULL,
  shape2 = NULL,
  scale2 = 1,
  delay = delay1,
  shape = shape1,
  scale = scale1
)
mweib_delayed(
  t = +Inf,
  delay1,
  shape1,
  scale1 = 1,
  delay2 = NULL,
  shape2 = NULL,
  scale2 = 1,
  delay = delay1,
  shape = shape1,
  scale = scale1
)

Value

Functions pertaining to the delayed Weibull distribution:

dweib_delayed gives the density
pweib_delayed gives the distribution function
qweib_delayed gives the quantile function
rweib_delayed generates a pseudo-random sample
mweib_delayed gives the restricted mean survival time

The length of the result is determined by n for rweib_delayed, and is the maximum of the lengths of the numerical arguments for the other functions, R's recycling rules apply.

Arguments

x: A numeric vector of values for which to get the density.
delay1: numeric. The first delay, must be non-negative.
shape1: numeric. First shape parameter, must be positive.
scale1: numeric. First scale parameter (inverse of rate), must be positive.
delay2: numeric. The second delay, must be non-negative.
shape2: numeric. The second shape parameter, must be non-negative.
scale2: numeric. The second scale parameter (inverse of rate), must be positive.
delay: numeric. Alias for first delay.
shape: numeric. Alias for first shape.
scale: numeric. Alias for first scale.
log: logical. Return value on log-scale?
q: A numeric vector of quantile values.
lower.tail: logical. Give cumulative probability of lower tail?
log.p: logical. P-value on log-sclae?
p: A numeric vector of probabilities.
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.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.