Every day at work we get a random cat fact in our slack chat, each fact has a number on it. Assuming those numbers start at 1, are unique, and are consecutive, how many cat facts total would you guess there are?

estimate_total_cat_facts.py

import math

def frequentist(facts):
  m = max(facts)
  k = len(facts)
  return m + (float(m) / k) - 1

def bayesian(facts):
  m = float(max(facts))
  k = float(len(facts))
  mean = (m - 1) * (k - 1) / (k - 2)
  variance = math.sqrt((k - 1) * (m - 1) * (m - k + 1) / (k - 3) / (k - 2) / (k - 2))
  return "%(mean)f +/- %(variance)f" % \
      {"mean": mean, "variance": variance}

estimators = [frequentist, bayesian]
seen_facts = [1, 6, 9, 23, 43, 32, 53, 16, 79, 14, 72, 41, 5]

print "Cat facts seen so far: " + str(seen_facts)
for estimator in estimators:
  print "Estimation using method '" + estimator.__name__ + "':",
  print estimator(seen_facts)

Cat facts seen so far: [1, 6, 9, 23, 43, 32, 53, 16, 79, 14, 72, 41, 5]
Estimation using method 'frequentist': 84.0769230769
Estimation using method 'bayesian': 85.090909 +/- 7.199174