"""
Benford's law in Python.
"""
import re
import matplotlib.pyplot as plot
from math import log10
def plot_benford(iterable):
"""Plot leading digit distribution in a string iterable.
"""
numbers = [float(n) for n in xrange(1, 10)]
# Plot the frequencies as predicted by the law.
benford = [log10(1 + 1 / d) for d in numbers]
plot.plot(numbers, benford, 'ro', label = "Predicted")
# Plot the actual digit frequencies.
data = list(digits(iterable))
plot.hist(data, range(1, 11), align = 'left', normed = True,
rwidth = 0.7, label = "Actual")
# Set plot parameters and show it in a window.
plot.title("Benford's Law")
plot.xlabel("Digit")
plot.ylabel("Frequency")
plot.xlim(0, 10)
plot.xticks(numbers)
plot.legend()
plot.show()
def digits(iterable):
"""Yield leading digits of number-like strings in an iterable.
"""
numexp = re.compile(r'\d+(\.\d+)?([eE]\d+)?')
leading = set("123456789")
for item in iterable:
for match in numexp.finditer(str(item)):
for digit in match.group(0):
if digit in leading:
yield int(digit)
break
if __name__ == "__main__":
import fileinput
plot_benford(fileinput.input())
