Yotta quantiles

yotta.py

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter
import math
N = 400      # number of tickets
i = 100000   # number of trials
k = 52       # number of weeks
rate = 0.002 # standard apr

M = N*25
elements = [0.1,0.15,0.75,10.0,0.4,15.0,0.0]
probabilities = [1.0/45.0, 1.0/73.0, 1.0/345.0,1.0/3935.0,1.0/165.0, 1/4518.0]
probabilities.append(1.0-sum(probabilities))

normalized_rate = (7.0*k)/365.0*rate

t = []
for i in range(i):
  t.append(sum(np.random.choice(elements, N*k, p=probabilities)))

a = np.array([x/M + normalized_rate for x in t]) 
print(np.percentile(a, 1))
print(np.percentile(a, 10))
print(np.percentile(a, 50))
print(np.percentile(a, 90))
print(np.percentile(a, 99))


def to_percent(y, position):
    s = str(math.floor(10000 * y)/100.0)
    if plt.rcParams['text.usetex'] is True:
        return s + r'$\%$'
    else:
        return s + '%'

# Generate data on commute times.
commutes = pd.Series(a)

commutes.plot.hist(grid=True, bins=30, rwidth=0.9,
                   color='#607c8e')
plt.title('APR for 100000 Trials')
formatter = FuncFormatter(to_percent)
plt.gca().xaxis.set_major_formatter(formatter)
plt.xlabel('APR')
plt.ylabel('Count')
plt.grid(axis='y', alpha=0)
plt.grid(axis='x', alpha=0)
plt.show()
plt.savefig('out.png')