Simulate a from a Poisson process
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
TRUErandomize 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.
Examples
## Sample homogenous Poisson process of rate 1/10
rxPp(10, 1 / 10)
#> [1] 12.38682 13.16377 27.35351 30.27454 34.06746 39.23769 58.13355
#> [8] 72.97714 102.32911 113.87403
## Sample inhomogenous Poisson rate of 1/10
rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#> [1] 60.28221 61.96611 62.71870 76.52984 87.25892 94.17678 100.00000
#> [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 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] 149.2766 291.7273 377.5511 497.7551 625.0034 666.2430 791.0833
#> [8] 846.1187 867.2486 1088.2302