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.

Author

Matthew Fidler

Examples

## Sample homogenous Poisson process of rate 1/10
rxPp(10, 1 / 10)
#>  [1]  14.83163  58.48428  84.19469  87.48909  90.52278  94.83410 104.91948
#>  [8] 110.53845 116.39847 126.72766

## Sample inhomogenous Poisson rate of 1/10

rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#>  [1]   5.323784  17.731921  23.915151  37.976382  45.883897  53.435959
#>  [7]  88.115709  90.911173  94.513078 100.000000

## 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 10 10 10 10 10 10 10 10 10

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

rxPp(10, 1 / 10, prob = function(x) {
  1/(1+abs(x))
})
#>  [1]   3.82921  18.66329  49.28656  67.50557  96.35750 199.78606 326.21669
#>  [8] 410.05275 627.77386 651.81652