Purpose
To generate poisson sample paths and explore density, cumulative density and view sample realizations of the poisson process

> library(ggplot2)
> n <- 20
> lambda <- 2
> z <- data.frame(x = 0:n, y1 = dpois(0:n, lambda), y2 = ppois(0:n,
+     lambda))
> p <- ggplot(z, aes(x = x))
> q1 <- p + geom_line(aes(y = y1), col = "sienna", lwd = 2)
> q2 <- p + geom_line(aes(y = y2), col = "sienna", lwd = 2)

Density

> print(q1)

Poisson-002.jpg

Cumulative Density

> print(q2)

Poisson-003.jpg

One poisson Sample path

> sample.path <- data.frame(x = 1:20, y = cumsum(rpois(20, 2)))
> p <- ggplot(sample.path, aes(x = x))
> q3 <- p + geom_step(aes(y = y))
> print(q3)

Poisson-004.jpg

Sample poisson paths with the mean line overlaid

> cols = rainbow(400)
> for (i in 1:400) {
+     plot(1:120, cumsum(rpois(120, 2)), type = "s", ylim = c(0,
+         300), col = cols[i], ylab = "", xlab = "")
+     par(new = T)
+ }
> abline(0, lambda, col = "black", lwd = 3)

Poisson-005.jpg