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code/lognormal_median_bootstrap.r

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+N <- 100
+Mu <- -0.5
+Sigma <- 2
+true.Median <- exp(Mu)
+#####
+X <- rlnorm(n = N, meanlog = Mu, sdlog = Sigma)
+
+### Assignment: assess the normal approximation
+
+###
+
+hist(X, probability = TRUE)
+m.hat <- median(X)
+
+Nboot <- 200
+npboot.ests <- rep(NA, Nboot)
+
+for(i in 1:Nboot){
+  Xrep <- sample(X, size = N, replace = TRUE)
+  npboot.ests[i] <- median(Xrep)
+}
+
+hist(npboot.ests, probability = TRUE, col ='lightblue2',
+     main = "Bootstrap estimates of the median")
+abline(v = m.hat, lwd = 3, lty = 2, col = "red")
+abline(v = true.Median, lwd = 3, lty = 3)
+legend(x = "topright",
+       legend = c("Point estimate", "True Median"),
+       col = c("red", "black"), lwd = 3,
+       lty = c(2, 3), bty = 'n')
+
+
+
+
+