Beta Distribution

beta.r

library(gtools)

step_length = 0.01

x = seq(0.0, 1.0, step_length)

a = 20.0
b = 2.0

beta_mean = a / (a + b)
print(beta_mean)
print(qbeta(beta_mean, a, b))

y = dbeta(x, a, b)
y_max = max(y)

k = binsearch(function(x) { x - beta_mean / step_length }, x / step_length)$where
k = k[length(k)] + 1

plot(smooth.spline(100.0 * x, y), type='l', xlab="LGD", ylab="Density")
polygon(100.0 * c(0.0, x[1:k], x[k]), c(0.0, y[1:k], 0.0), col='gray')

# add average line
lines(100.0 * x[k] * c(1.0, 1.0), c(0.0, y_max), lty=2)
text(100.0 * x[k], y_max + 0.1, labels=c('mean'))