Show code cell source Hide code cell source

import pandas as pd
import numpy as np
import random

5.11. JNB Lab Solutions

Exercise 1a

1. Read in Homicide data and drop rows that have missing data.

Show code cell source Hide code cell source

Hom=pd.read_excel('homicides.xlsx') #read data file
Hom=Hom[Hom["Manner of Death"]=='HOMICIDE']
Hom=Hom[["Date of Incident","Age","Gender","Race","Primary Cause","Residence City","Incident Zip Code"]]
Hom=Hom.dropna()
Hom.head(1)

	Date of Incident	Age	Gender	Race	Primary Cause	Residence City	Incident Zip Code
0	2017-02-26 10:48:00	23.0	Male	Black	MULTIPLE GUNSHOT WOUNDS	Chicago	60623.0

2. Extract the month and year of homicide incidents.

Show code cell source Hide code cell source

from datetime import datetime
Hom['new_date'] = [d.date() for d in Hom['Date of Incident']] 
dates=Hom['new_date'].values
year=[my_str.year for my_str in dates]
month=[my_str.month for my_str in dates]
day=[my_str.day for my_str in dates]
Hom['year'] = year
Hom['month'] = month
Hom['day'] = day
Hom.head(1)

	Date of Incident	Age	Gender	Race	Primary Cause	Residence City	Incident Zip Code	new_date	year	month	day
0	2017-02-26 10:48:00	23.0	Male	Black	MULTIPLE GUNSHOT WOUNDS	Chicago	60623.0	2017-02-26	2017	2	26

3. Get Chicago data, select the columns [“Age”,“Gender”,“Race”,“Primary Cause”,“Incident Zip Code”,“year”,“month”,“day”] and use integer format

Show code cell source Hide code cell source

ChiHom=Hom[Hom["Residence City"]=='Chicago'] #get data for just Chicago
df=ChiHom[["Age","Gender","Race","Primary Cause","Incident Zip Code","year","month","day"]]
df=df.dropna()
df['year']=df['year'].astype(int)
df['month']=df['month'].astype(int)
df['day']=df['day'].astype(int)
df['Age']=df['Age'].astype(int)
df['Incident Zip Code']=df['Incident Zip Code'].astype(int)
df=df[df["year"]>2014]
df.head(1)

	Age	Gender	Race	Primary Cause	Incident Zip Code	year	month	day
0	23	Male	Black	MULTIPLE GUNSHOT WOUNDS	60623	2017	2	26

4. Get the number of Chicago homicides in July 2020.

Show code cell source Hide code cell source

july=df[df["month"]==7]
july20=july[july["year"]==2020]
print("Chicago Homicides In July 2020: ",len(july20))

Chicago Homicides In July 2020:  89

5. Get the number of homicides which occurred on each day of July between 2015 and 2019.

Show code cell source Hide code cell source

julydf=july
julydf=julydf.reset_index(drop=True)
julycount=pd.Series(np.arange(0,155,1))
julycount[:]=0
j=0
for year in np.arange(2015,2020,1):
    for day in np.arange(1,32,1):
        for i in julydf.index:
            if julydf.loc[i,"day"]==day and julydf.loc[i,"year"]==year:
                julycount[j]=julycount[j]+1
        j=j+1
print(julycount[0:5])

0    0
1    1
2    3
3    1
4    4
dtype: int32

6. Get frequency distributions for the number of homicides in a day

Show code cell source Hide code cell source

jm=julycount.max()
julyfreq=pd.Series(np.arange(0,jm+1,1))  #create a series with index the number of homicides and value equal to the frequency
julyfreq[:]=0
dj=julycount
for i in julycount.index:
    for j in np.arange(0,jm+1,1):
        if dj[i]==j:
            julyfreq[j]=julyfreq[j]+1
s=julyfreq.sum()
julyfreq=julyfreq/s
print(julyfreq)
julyfreq[0]

0    0.200000
1    0.309677
2    0.258065
3    0.141935
4    0.051613
5    0.012903
6    0.012903
7    0.012903
dtype: float64

0.2

7. Do a Monte Carlo simulation for monthly homicide counts in July based on 31 random draws from the respective empirical distributions.

Show code cell source Hide code cell source

n = random.random()
nummonths=10000
numdays=31*nummonths
julydaytotal=pd.Series(np.arange(0,numdays,1))
julydaytotal[:]=0

for i in np.arange(0,numdays,1):
    x=random.random()
    exit=0
    cum=0
    for j in julyfreq.index:
        if x< cum+julyfreq[j] and exit==0:
            julydaytotal[i]=j
            exit=1
        else:
            cum=cum+julyfreq[j]


julymonths=pd.Series(np.arange(0,nummonths,1))
julymonths[:]=0
i=0
for month in np.arange(0,nummonths,1):
    sum=0
    for j in np.arange(0,31,1):
        sum=sum+julydaytotal[i]
        i=i+1
    julymonths[month]=sum
    month=month+1

8. Make a histogram for July.

Show code cell source Hide code cell source

import matplotlib.pyplot as plt
#Make Histogram
fig, ax = plt.subplots()
n,bins,patches = ax.hist(julymonths, bins=10,density=1,alpha=.5)
plt.xlabel("July Homicide Count")
plt.ylabel("Proportion")
plt.title("10,000 Simulated July Homicide Counts based on 2015-2019 Data")

Text(0.5, 1.0, '10,000 Simulated July Homicide Counts based on 2015-2019 Data')

Exercise 1b

b) Find the empirical p-value of getting at least 108 homicides (the number in July 2020.)

Show code cell source Hide code cell source

julycount=julymonths[julymonths>=108]
pjuly=len(julycount)/10000
print("Probaility that a random draw of 31 days from July 2015-2020 distibution results in 85 or more homicides:",pjuly)

Probaility that a random draw of 31 days from July 2015-2020 distibution results in 85 or more homicides: 0.0

Exercise 2

a) Make a histogram of the difference July homicide count - May homicide count

Show code cell source Hide code cell source

maydf=df[df["month"]==5]
maydf=maydf.reset_index(drop=True)
maycount=pd.Series(np.arange(0,155,1))
maycount[:]=0
j=0
for year in np.arange(2015,2020,1):
    for day in np.arange(1,32,1):
        for i in maydf.index:
            if maydf.loc[i,"day"]==day and maydf.loc[i,"year"]==year:
                maycount[j]=maycount[j]+1
        j=j+1
mm=maycount.max()
mayfreq=pd.Series(np.arange(0,mm+1,1))  #create a series with index the number of homicides and value equal to the frequency
mayfreq[:]=0
dm=maycount
for i in maycount.index:
    for j in np.arange(0,mm+1,1):
        if dm[i]==j:
            mayfreq[j]=mayfreq[j]+1
s=mayfreq.sum()
mayfreq=mayfreq/s
n = random.random()
nummonths=10000
numdays=31*nummonths
maydaytotal=pd.Series(np.arange(0,numdays,1))
maydaytotal[:]=0

for i in np.arange(0,numdays,1):
    x=random.random()
    exit=0
    cum=0
    for j in mayfreq.index:
        if x< cum+mayfreq[j] and exit==0:
            maydaytotal[i]=j
            exit=1
        else:
            cum=cum+mayfreq[j]


maymonths=pd.Series(np.arange(0,nummonths,1))
maymonths[:]=0
i=0
for month in np.arange(0,nummonths,1):
    sum=0
    for j in np.arange(0,31,1):
        sum=sum+maydaytotal[i]
        i=i+1
    maymonths[month]=sum
    month=month+1

Show code cell source Hide code cell source

diff=julymonths-maymonths
import matplotlib.pyplot as plt
#Make Histogram
fig, ax = plt.subplots()
n,bins,patches = ax.hist(diff, bins=10,density=1,alpha=.5)
plt.xlabel("Difference in Homicide Counts")
plt.ylabel("Proportion")
plt.title("Simulated Difference between the May and July Homicide Counts")
plt.savefig("Diff.png")

Find the probability that July will have at least n more homicides than May \((0\le n \le 20)\).

Show code cell source Hide code cell source

pdiff=pd.Series(np.arange(0,21,1))
for i in pdiff.index:
    pdiff.loc[i]=len(diff[diff>=i])/10000
pdiff

0     0.7409
1     0.7091
2     0.6766
3     0.6436
4     0.6077
5     0.5694
6     0.5298
7     0.4885
8     0.4529
9     0.4168
10    0.3796
11    0.3436
12    0.3082
13    0.2773
14    0.2459
15    0.2171
16    0.1889
17    0.1677
18    0.1461
19    0.1246
20    0.1045
dtype: float64

b) Make a plot of these probabilities

Show code cell source Hide code cell source

%matplotlib notebook
import matplotlib as mpl
import matplotlib.pyplot as plt

plt.plot(pdiff, 'o-',color='k')
for i in pdiff.index:
    plt.text(i,pdiff[i]+.01, str(pdiff[i]),color='r',size=6)
    plt.text(i-.2,pdiff[i]-.03, str(i),color='k',size=6)
    
plt.xlabel("Number More Homicides in July than in May")
plt.ylabel("Estimated Probability Based on 2015-2019 Data")
xl = np.arange(21)
plt.xticks(xl, xl, alpha=0.7,size=5)
plt.title("Probability that Chicago's July Homicide Count Exceeds May Homicide Count",size=8)
plt.savefig("MayvsJuly.png")

c) Based on 2015-2019 data, there is a 10% chance of 20 more homicides in July than May.