R27. Cauchy Distribution in R

The Cauchy Cumulative Distribution Function is:

We use this formula as well as pcauchy function in the plot, and the two lines are plotted with different linewidths.

# ex27.R
N <- 500
gamma <- 2
x0 <- 3
x <- seq(-5*gamma+x0,+5*gamma+x0,length.out = N)
y <- 1/pi*atan((x-x0)/gamma) + 0.5
main <- sprintf('Cauchy CDF, gamma = %.1f, and x0 = %.1f',
                gamma, x0)
plot(x,y, col = 'black', lwd = 10)
lines(x,pcauchy(x,location = x0, scale = gamma),
      col = 'green', lwd = 5)
title(main = main)

Output: