Simulation of a Poisson process — poisson_process

Simulates event times from a (one-dimensional, homogeneous) Poisson process of rate \(\lambda\) per hour. The user has the options to simulate events over a fixed time period of hours hours or to simulate a fixed number n_events of events.

poisson_process_sim(lambda = 1, hours = 24, n_events = NULL)

Arguments

lambda: A positive numeric scalar. The rate of the Poisson process.
hours: A positive integer scalar. The number of hours for which to simulate a Poisson process of rate \(\lambda\) events per hour.
n_events: A positive integer scalar. The number of events to simulate.

Value

A numeric vector containing the (ordered, smallest to largest) times at which the events occur. The returned object has class "poisson_process".

Details

If n_events is supplied then exactly n_events are simulated and hours has no effect. If n_events is not supplied then events are simulated over the time interval (0, hours). If no events occur in (0, hours) then the value \(-1\) is returned.

Examples

sim1 <- poisson_process_sim(lambda = 2, hours = 24)
plot(sim1)


sim2 <- poisson_process_sim(lambda = 2, n_events = 50)
plot(sim2)