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) = lambda

*gamma*(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] 57.27572 85.13706 90.54349 109.02733 116.44621 119.69145 122.37819
#> [8] 128.28736 140.42346 151.35881
## Sample inhomogenous Poisson rate of 1/10
rxPp(10, 1 / 10, gamma = 2, tmax = 100)
#> [1] 13.29608 33.67876 34.44031 47.24732 66.89399 75.32935 85.52547 86.33391
#> [9] 89.18935 91.71946
## 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] 1.085674 7.565262 143.229471 203.243288 214.208926 221.753931
#> [7] 447.697011 485.449098 588.480109 634.791204
```