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
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.
Examples
## Sample homogenous Poisson process of rate 1/10
rxPp(10, 1 / 10)
#> [1] 0.1418592 3.0551066 17.5266217 18.9209061 23.5764622 32.0313849
#> [7] 34.5432774 39.6298088 58.8308591 58.9267474
## Sample inhomogenous Poisson rate of 1/10
rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#> [1] 55.09252 90.40874 96.89581 99.67418 100.00000 100.00000 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] 11.89423 114.97292 279.79528 331.31831 370.20997 480.07313 604.24600
#> [8] 633.01980 797.29489 799.28924