import numpy as np
import matplotlib.pyplot as plt


def first_est(data):
    sum = 0
    for x in data:
        sum += x
    sum = sum / len(data)
    sum = sum * 2
    return sum - 1

def second_est(data):
    n = len(data)
    max = np.amax(data)
    max = max * (n + 1)
    max = max / n
    return max - 1

def generate_first_est(m, n):
    d = []
    for x in range(0, n):
        d.append(abs(m - first_est(np.random.randint(m, size=n))))
    return d

def generate_second_est(m, n):
    d = []
    for x in range(0, n):
        d.append(abs(m - second_est(np.random.randint(m, size=n))))
    return d

smeans = []
for k in range(0, 500):
    smeans.append(np.mean(generate_second_est(1000, k)))

plt.plot(smeans, linewidth=2)
plt.show()

fv = np.var(generate_first_est(1000, 500))
sv = np.var(generate_second_est(1000, 500))
print("first_est var:", fv, "<> second_est var:", sv)
# first_est var: 213.124099298 <> second_est var: 3.87214624282
# So, the second estimator is more effective (because has much lower variance).