1-dimensional Point-Process in R (spatstat)

Question

I have asked another question, which was closed as Too Broad. Now, I will try to specify.

Again, I would like to simulate a 1-dimensional point process in R. So far, I've only been working on 2-dimensional simulations and would need a bit of help.

My goal is a simulation like in the picture

But, I only need the real line with the random points on it.

I use spatstat and have already found out that I can generate random points on a 1-dim Line with:

rpoisppOnLines(lambda, L, lmax = NULL, ..., nsim=1, drop=TRUE)

Now, I would like to produce the real line, preferably with matching labeling.

Does anyone have an idea?

Answer 1

Here is some crude code on getting samples from a point process.

library(spatstat)
lambda = 5
L = psp(0, 0, 3, 0, owin(c(0, 3), c(-1, 1)))
pp = rpoisppOnLines(lambda, L, lmax = NULL, nsim=1, drop=TRUE)
plot(pp$x, pp$y, pch = 4, lwd = 2, cex = 2)
abline(0, 0)

You could make your plot fancy with ggplot2

Answer 2

You could use a simple linear network to represent the one dimensional line segment you want to simulate on. This also makes it possible to fit models (lppm), estimate the intensity non-parametrically (density.lpp), estimate the K-function (linearK), and a bunch of other things:

library(spatstat)
x_start <- 0
x_end <- 3
endpoints <- ppp(x=c(x_start, x_end), y=c(0,0), window = owin(c(x_start, x_end), c(-.1,.1)))
L <- linnet(endpoints, edges = matrix(c(1,2),ncol = 2))
X <- rpoislpp(lambda = 5, L = L)

However, this tool is designed for points on a complicated network and not just the real line, so the plotting method is not really adapted to this setting, and might not produce exactly what you want (too much white space):

plot(X, pch = 4, lwd = 2, main = "")
axis(1)

You can extract the coordinates of the point pattern using coords and then use the plotting method from the other answer from there:

co <- coords(X)
co$x
#> [1] 1.3306861 2.5550691 1.7776248 2.9486675 1.8571362 2.5020587 1.4843001
#> [8] 0.4371669 0.8478670

^{Created on 2018-12-18 by the reprex package (v0.2.1)}