I am trying to simulate number of claims in next 12 months using a homogeneous poisson process following the R codes:

`lambda <- 17 # the length of time horizon for the simulation T_length <- 31 last_arrival <- 0 arrival_time <- c() inter_arrival <- rexp(1, rate = lambda) while (inter_arrival + last_arrival < T_length) { last_arrival <- inter_arrival + last_arrival arrival_time <- c(arrival_time,last_arrival) inter_arrival <- rexp(1, rate = lambda) } `

And I get a list with around 500 elements, then I repeat this for each of the twelve months, how do I plot the trajectory of the counting process?

**Contents**hide

#### Best Answer

The following code plots a line chart with the appropriate jumps.

`n <- length(arrival_time) counts <- 1:n plot(arrival_time, counts, pch=16, ylim=c(0, n)) points(arrival_time, c(0, counts[-n])) segments( x0 = c(0, arrival_time[-n]), y0 = c(0, counts[-n]), x1 = arrival_time, y1 = c(0, counts[-n]) ) `

### Similar Posts:

- Solved – Manually simulating Poisson Process in R
- Solved – Fit inter-arrival time to Poisson Distribution/Exponential
- Solved – Non homogenous Poisson process with simple rates
- Solved – the difference between time, arrival-time, and inter-arrival-time is poisson process
- Solved – Variance of arrival process with shifted exponential distribution