# rm(list=ls())
options(OutDec = ",") 
#==============================================================================
# Exemplo:
#
# Aproximacao assintotica lognormal
#
#==============================================================================
# Amostra n=1 e y=3.
#==============================================================================
y       <- 3
a       <- 3             # Hiperparametros (priori)
b       <- 3             # Hiperparametros (priori)
x       <- seq(-2,6,0.01) 
lambda1 <- dgamma(x,a+y,b+1)

#------------------------------------------------------------------------------
# Aproximacao normal
#------------------------------------------------------------------------------
media1  <- (a+y-1)/(b+1)
var1    <- media1/(b+1)
lambda2 <- dnorm(x,media1,sqrt(var1))

#------------------------------------------------------------------------------
# Aproximacao lognormal
#------------------------------------------------------------------------------
media2  <- log((a+y)/(b+1))
var2    <- 1/(a+y)
lambda3 <- dlnorm(x,media2,sqrt(var2))

#==============================================================================
# Grafico para comparacao
#==============================================================================
par(mfrow=c(1,1),lwd=2.0,cex.lab=1.5,cex.axis=1.5,
    lab=c(10,6,5),mar=c(5,5,2,2.5),xpd=T,cex.main=2.0,bty="n")
plot(x,lambda1,type="l",lwd=4,col="black",xlab=expression(lambda),
  ylab=expression(paste("f(",lambda,"|y)",sep=" ")),ylim=c(0,0.8))
lines(x,lambda2,lwd=4,col="red",lty=2)
lines(x,lambda3,lwd=4,col="blue",lty=2)
legend("topright",legend=c("Verdadeira","Aprox. Normal",
      "Aprox. Lognormal"),
       col=c("black","red","blue"),lty=c(1,2,2),lwd=c(4,4,4),bty="n",cex=1.5)

# rm(list=ls()) 
#==============================================================================
# graphics.off()
#==============================================================================
# Fim
#==============================================================================