# HG changeset patch
# User Brian Neal <bgneal@gmail.com>
# Date 1357611032 21600
# Node ID 5a9a6d1dbf1b51d2c7313a936d8921e45c505e89
# Parent  65b70b4e12adec2bc66a89b7f3377aa683847b70
Chapter 5.4, exercise 4, Pareto distributions.

diff -r 65b70b4e12ad -r 5a9a6d1dbf1b ch5ex4.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/ch5ex4.py	Mon Jan 07 20:10:32 2013 -0600
@@ -0,0 +1,52 @@
+"""Chapter 5.3 exercise 4 in Allen Downey's Think Complexity book.
+
+"Write a version of plot_ccdf that plots the complementary CCDF on a log-log
+scale.
+
+To test your function, use paretovariate from the random module to
+generate 100 values from a Pareto distribution. Plot the CCDF on a log-y scale
+and see if it falls on a straight line. What happens to the curve as you
+increase the number of values?"
+
+"""
+import random
+import sys
+
+import matplotlib.pyplot as pyplot
+
+
+def plot_ccdf_log_log(x_vals, y_vals, title=''):
+    """Given a set of x-values and y-values from a continuous distribution, plot
+    the complementary distribution (CCDF) on a log-log scale.
+
+    """
+    if len(x_vals) != len(y_vals):
+        raise ValueError
+
+    ys = [1.0 - y for y in y_vals]
+
+    pyplot.clf()
+    pyplot.xscale('log')
+    pyplot.yscale('log')
+    pyplot.title(title)
+    pyplot.xlabel('x')
+    pyplot.ylabel('1-y')
+    pyplot.plot(x_vals, ys, label='1-y', color='green', linewidth=3)
+    pyplot.legend(loc='upper right')
+    pyplot.show()
+
+
+def main(script, n, alpha):
+
+    n = int(n)
+    alpha = float(alpha)
+
+    x_vals = range(n)
+    y_vals = [random.paretovariate(alpha) for x in x_vals]
+    y_vals.sort(reverse=True)
+
+    plot_ccdf_log_log(x_vals, y_vals, 'paretovariate w/alpha = {}'.format(alpha))
+
+
+if __name__ == '__main__':
+    main(*sys.argv)