Solved problem 8.

8/script.R

@@ -0,0 +1,44 @@
+#!/bin/env Rscript
+
+# Libraries
+library("pracma")
+library("ggplot2")
+
+# Set the seed for the RNG
+set.seed(2009)
+
+cauchy_location <- 1
+cauchy_scale <- 1.8
+cauchy_gen <- rcauchy(n = 107, location = cauchy_location, scale = cauchy_scale)
+cauchy_gen <- sort(cauchy_gen)
+
+quantile_idxs <- 1:107 / (107 + 1)
+
+cauchy_quantiles <- sapply(quantile_idxs, function(p) {
+    cauchy_location + cauchy_scale * tan(pi * (p - 0.5))
+})
+
+norm_mean <- -2.8
+norm_var <- 1.4
+norm_quantiles <- sapply(quantile_idxs, function(p) {
+    norm_mean + sqrt(2 * norm_var) * erfinv(2 * p - 1)
+})
+
+df <- data.frame(
+    quantile_idxs = quantile_idxs,
+    cauchy_gen = cauchy_gen,
+    cauchy_quantiles = cauchy_quantiles,
+    norm_quantiles = norm_quantiles
+)
+
+#  Then plot them and save the output
+plot <- ggplot(df, aes(x = quantile_idxs)) +
+    geom_line(aes(y = cauchy_gen, color = "Generated")) +
+    geom_line(aes(y = cauchy_quantiles, color = "Cauchy Quantiles")) +
+    geom_line(aes(y = norm_quantiles, color = "Normal Quantiles")) +
+    xlab("Quantiles") +
+    ylab("") +
+    scale_color_manual(values = c("red", "blue", "green")) +
+    theme(legend.title = element_blank())
+
+ggsave(plot = plot, "output.png")

README.md

@@ -12,6 +12,10 @@ https://docs.google.com/document/d/1kS8zsUVcjWqqpty2CcXHi8jTA-QsOA_2Q0VsUJ4OfXM
 
 https://docs.google.com/document/d/1DnvOxo3GlUY7sBHUCcyMEbMlQE2AYFBWAOSrNZyb4d4
 
+## 8
+
+https://docs.google.com/document/d/1x_AsfHc4JNxV8P6oOfUoZCu1yLQ9TQ82zRSoT7pDRrM
+
 # Util
 
 ## 6