Simulate a from a Poisson process

Simulate a from a Poisson process

Usage

rxPp(
  n,
  lambda,
  gamma = 1,
  prob = NULL,
  t0 = 0,
  tmax = Inf,
  randomOrder = FALSE
)

Arguments

n

Number of time points to simulate in the Poisson process

lambda

Rate of Poisson process

gamma

Asymmetry rate of Poisson process. When gamma=1.0, this simulates a homogenous Poisson process. When gamma<1.0, the Poisson process has more events early, when gamma > 1.0, the Poisson process has more events late in the process.

When gamma is non-zero, the tmax should not be infinite but indicate the end of the Poisson process to be simulated. In most pharamcometric cases, this will be the end of the study. Internally this uses a rate of:

l(t) = lambdagamma(t/tmax)^(gamma-1)

prob

When specified, this is a probability function with one argument, time, that gives the probability that a Poisson time t is accepted as a rejection time.

t0

the starting time of the Poisson process

tmax

the maximum time of the Poisson process

randomOrder

when TRUE randomize the order of the Poisson events. By default (FALSE) it returns the Poisson process is in order of how the events occurred.

Value

This returns a vector of the Poisson process times; If the dropout is >= tmax, then all the rest of the times are = tmax to indicate the dropout is equal to or after tmax.

See also

Other Variability and uncertainty: confint.rxSolve(), cvPost(), dfWishart(), rinvchisq(), rxEtaDistExpand(), rxEtaDistMuRef(), rxRmvn(), rxRmvt(), rxSimThetaOmega(), rxUiEtaDistAnchors(), rxUiEtaDists(), swapMatListWithCube()

Author

Matthew Fidler

Examples

## Sample homogenous Poisson process of rate 1/10
rxPp(10, 1 / 10)
#>  [1]  6.077768 22.665782 23.617748 23.713796 28.247910 51.302167 73.913293
#>  [8] 76.775997 79.789859 79.927935

## Sample inhomogenous Poisson rate of 1/10

rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#>  [1]  23.13272  38.67615  55.22575  56.08766  76.99928  79.80645  80.83790
#>  [8] 100.00000 100.00000 100.00000

## Typically the Poisson process times are in a sequential order,
## using randomOrder gives the Poisson process in random order

rxPp(10, 1 / 10, gamma = 2, tmax = 10, randomOrder = TRUE)
#>  [1] 10.000000 10.000000 10.000000 10.000000 10.000000 10.000000 10.000000
#>  [8]  8.355783  6.073167 10.000000

## This uses an arbitrary function to sample a non-homogenous Poisson process

rxPp(10, 1 / 10, prob = function(x) {
  1/(1+abs(x))
})
#>  [1]    3.894435   42.205721  194.470466  334.969363  437.481336  496.269052
#>  [7]  505.971079  665.989759  834.522203 1062.614359