"""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)