Solved – Trajectory of homogeneous poisson process

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?

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]) ) 

Output: enter image description here

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