'''Challenge 0: Create a new script and add a multi-line comment

at the top with the name of the workshop, your name, and the date.

Save the script in your Python script folder.

'''

'''Challenge 1: Import math, matplotlib.pyplot as plt, pandas as pd,

scipy.stats as stats.

'''

import math
import matplotlib.pyplot as plt
import pandas as pd
import scipy.stats as stats
import numpy as np

'''Challenge 2: Read "OR Cases 3.csv" into a DataFrame.'''

df = pd.read_csv("OR-Cases-3.csv")
print (df.head())

'''Challenge 3: Sum the number of OR cases by week of year.

DOC: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.core.groupby.GroupBy.sum.html

TUTORIAL: https://www.shanelynn.ie/summarising-aggregation-and-grouping-data-in-python-pandas/

'''
sum_cases_by_week = df.groupby("Week").agg({'Number.of.cases': sum})
print (sum_cases_by_week)

'''Challenge 4: Create a histogram of the number of cases by week.

Q: Does this look Poisson? Normal?
A: No, it doesn't look poisson nor normal.

'''

plt.hist(df["Number.of.cases"], facecolor='blue')
plt.show()

'''Challenge 5: Suppose the data is Poisson.

(a) Estimate the Poisson parameter, lambda.

(b) Estimate the 95% confidence interval of lambda.

HINT: https://stats.stackexchange.com/questions/15371/how-to-calculate-a-confidence-level-for-a-poisson-distribution

'''

# (a)
n = len(sum_cases_by_week["Number.of.cases"])
poi_lambda = sum(sum_cases_by_week["Number.of.cases"] / float(n))
conf_interval = (poi_lambda - 1.96 * math.sqrt(poi_lambda / n), poi_lambda + 1.96 * math.sqrt(poi_lambda / n))
print ("Lambda: {} ".format(poi_lambda))
print ("95% Confidence Interval: {}".format(conf_interval))

'''Challenge 6: We would prefer that the weekly arrivals be Markovian

so we can use M/M/c queueing models. Arrivals are Markovian

if the time between arrivals is exponentially distributed or,

equivalently, the number of arrivals by day is Poisson

distributed.

Let's see if the weekly number of OR cases follows a Poisson distribution.

Unfortunately, Python doesn't (yet) have an easy way of doing this so we need

to do a little programming.

We will perform a chi-squared analysis that compares the actual to expected

numbers of observations falling into 10 equal-width bins.

Create the bins:

(a) Calculate the minimum and maximum number of weekly cases.

(b) Calculate the bin width as (max - min) / 10.

(c) Each bin has a left and right cutoff point. Create a list of 10 right

cutoff points for the bins.

'''
min_cases_weekly = min(sum_cases_by_week["Number.of.cases"])
max_cases_weekly = max(sum_cases_by_week["Number.of.cases"])
bin_width = math.ceil((max_cases_weekly - min_cases_weekly

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