docc: The Extended Occupancy Distribution

In occupancy: Probability Functions for Occupancy Distributions

Description

Density, distribution function, quantile function and random generation for the extended occupancy distribution with size and shape parameters.

Usage

docc(x, size, space, prob = 1, approx = FALSE, log = FALSE)

docc.all(max.size, space, prob = 1, approx = FALSE, log = FALSE)

pocc(
  x,
  size,
  space,
  prob = 1,
  approx = FALSE,
  log.p = FALSE,
  lower.tail = TRUE
)

qocc(
  p,
  size,
  space,
  prob = 1,
  approx = FALSE,
  log.p = FALSE,
  lower.tail = TRUE
)

rocc(n, size, space, prob = 1)

Arguments

x	vector of quantiles.
size	The size parameter for the occupancy distribution (number of balls)
space	The space parameter for the occupancy distribution (number of bins)
prob	The probability parameter for the occupancy distribution (probability of ball occupying its bin)
approx	A logical value specifying whether to use the normal approximation to the occupancy distribution
log	logical; if TRUE, probabilities p are given as log(p).
max.size	The maximum size parameter for the occupancy distribution (number of balls)
log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

docc.all returns the entire PMF.

Value

If all inputs are correctly specified (i.e., parameters are in allowable range and arguments are integers) then the output will be a vector of probabilities/log-probabilities corresponding to the vector argument x

References

O'Neill, B. (2021) Three distributions in the extended occupancy problem.

Examples

x <- rocc(10, 2, 2)
p <- pocc(x, 2, 2)
stopifnot(x == qocc(p, 2, 2))
docc.all(2,2)

occupancy documentation built on June 24, 2021, 5:06 p.m.