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] 5.323784 21.415131 37.478421 40.945143 59.422799 85.409544
#> [7] 102.011935 129.996616 142.404753 154.641998
## Sample inhomogenous Poisson rate of 1/10
rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#> [1] 26.07947 33.48687 54.82623 58.40640 60.65105 60.98144 61.70869 62.79017
#> [9] 67.64753 76.77842
## 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] 0.4752658 147.5966580 186.9155552 205.7920579 220.3607906 305.9780282
#> [7] 361.3626502 404.7342404 606.5618198 690.6836285