## code to accompany the Normal density/distr
## example from lecture 2 of PSTAT 215A, 
## Bayesian Inference, UCSB
##
## Robert B. Gramacy adapted from Peter Hoff


## Generating figure 2.2 from book
par(mfrow=c(1,2))

## setting up the y-vaues, the mean, and sd
y <- seq(8,14,length=1000)
mu <- 10.75
sigma <- sqrt(0.64)

## making two plots
plot(y, pnorm(y, mu, sigma), type="l", lwd=2, xlab="y", ylab="F(y)")
abline(h=c(0,0.5,1), col="gray")
plot(y, dnorm(y, mu, sigma), type="l", lwd=2, xlab="y", ylab="f(y)")
abline(v=mu, col="gray")

## comparing normal to log normal (Fig 2.3)
par(mfrow=c(1,2), bty="n")
plot(y, dnorm(y, mu, sigma), type="l", lwd=2, xlab="y", ylab="f(y)",
     main="normal")
abline(v=c(mu, mu, mu), col=1:3, lty=1:3, lwd=2)
sigma.2 <- 0.8
y2 <- seq(0, 300000, length=1000)
f2 <- dlnorm(y2, mu, sigma.2)
plot(y2, 10^5*f2, type="l", lwd=2, xlab="y", ylab="10^5*f(y)",
     main="log-normal")
m <- exp(mu + 0.5*0.8*sigma.2^2)
med <- exp(mu)
mode <- y2[which.max(f2)]
abline(v=c(m, med, mode), col=1:3, lty=1:3, lwd=2)
legend("topright", c("mean", "median", "mode"), col=1:3, lty=1:3, lwd=2)