Examples: Poission distribution as applied to the 100-year flood. https://tonyladson.wordpress.com/2015/06/29/100-year-flood-poisson-distribution/

OneHundredYearPoisson.R

dpois(0,1)  # prob of zero 100-year floods in 100 years
dpois(0,1)  # prob of zero 100-year floods in 100 years
[1] 0.3678794
dpois(1,1)  # prob of one 100-year floods in 100 years
[1] 0.3678794
dpois(2,1)  # prob of two 100-year floods in 100 years
[1] 0.1839397


# simulation

library(ggplot2)
df <- expand.grid(x = 1:10, y = 1:10)
df$z <- rbinom(100, 100, 0.01) # could also use rpois(100,1)


ggplot(data=df, aes(x,y)) + geom_tile(aes(fill=z)) + 
  scale_fill_gradient(low="green", high = "red", name = 'Floods') +
  geom_text(data = df, aes(x, y, label = z)) +
  scale_x_continuous(breaks = NULL) +
  scale_y_continuous(breaks = NULL) +
  xlab('') +
  ylab('') 



set.seed(2000)
rpois(10, 1)
[1] 0 1 0 1 2 1 3 1 2 1
# number of 100-year floods in each of 10 100-year sequences