From d5962d232258996da4969fe00b4fd117d003e479 Mon Sep 17 00:00:00 2001
From: Connor Moore <connor@hhmoore.ca>
Date: Sat, 25 Apr 2026 21:38:01 -0400
Subject: Finished section 2 and section 3

---
 .../figures/tracy-widom-approx/plot_tracy_widom.m  | 41 ++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 report/figures/tracy-widom-approx/plot_tracy_widom.m

(limited to 'report/figures/tracy-widom-approx/plot_tracy_widom.m')

diff --git a/report/figures/tracy-widom-approx/plot_tracy_widom.m b/report/figures/tracy-widom-approx/plot_tracy_widom.m
new file mode 100644
index 0000000..c43e3f6
--- /dev/null
+++ b/report/figures/tracy-widom-approx/plot_tracy_widom.m
@@ -0,0 +1,41 @@
+close all;
+clear; clc;
+
+x = linspace(-6,4,1000)
+
+[pdf1,~] = tracywidom_appx(x,1)
+[pdf2,~] = tracywidom_appx(x,2)
+[pdf4,~] = tracywidom_appx(x,4)
+
+% Fig. 1 Tracy-Widoms
+figure(1)
+hold on
+plot(x,pdf1)
+plot(x,pdf2)
+plot(x,pdf4)
+
+A = [x', pdf1', pdf2', pdf4']
+save -ascii tracy_widom.txt A
+
+% Fig 2. Compare to Normal
+normpdf = @(x,mu,sigma) 1/(sigma*sqrt(2*pi)).*exp(-0.5*((x-mu)/sigma).^2)
+npdf = normpdf(x,-1.38,1.268)
+
+figure(2)
+hold on
+plot(x,pdf1)
+plot(x,npdf,'--')
+
+B = [x', pdf1', npdf']
+save -ascii tracy_widom_normal.txt B
+
+% Skewness and Excess Kurtosis
+x_stat = linspace(-9,9,50e3)
+[pdf1_stat,~] = tracywidom_appx(x_stat,1)
+npdf_stat = normpdf(x_stat, -1.38, 1.268)
+
+fprintf("Tracy Widom\n")
+[~,~] = pdf_stats(x_stat, pdf1_stat)
+fprintf("Normal Distribution\n")
+[~,~] = pdf_stats(x_stat, npdf_stat)
+
-- 
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