How to plot cumulative distribution function in python for six sided dice simulation?

Question

I am trying to

1. Plot histogram with frequencies of dice sum outcomes from the simulation.
2. Calculate and plot cumulative distribution function.
3. find and plot median.

So Far this is what I have:

import pylab
import random

sampleSize = 100


## Let's simulate the repeated throwing of a single six-sided die
singleDie = []
for i in range(sampleSize):
    newValue = random.randint(1,6)
    singleDie.append(newValue)

print "Results for throwing a single die", sampleSize, "times."
print "Mean of the sample =", pylab.mean(singleDie)
print "Median of the sample =", pylab.median(singleDie)
#print "Standard deviation of the sample =", pylab.std(singleDie)
print
print

pylab.hist(singleDie, bins=[0.5,1.5,2.5,3.5,4.5,5.5,6.5] )
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('singleDie.png')
pylab.show()




## What about repeatedly throwing two dice and summing them?
twoDice = []
for i in range(sampleSize):
    newValue = random.randint(1,6) + random.randint(1,6)
    twoDice.append(newValue)



print "Results for throwing two dices", sampleSize, "times."
print "Mean of the sample =", pylab.mean(twoDice)
print "Median of the sample =", pylab.median(twoDice)
#print "Standard deviation of the sample =", pylab.std(twoDice)

pylab.hist(twoDice, bins= pylab.arange(1.5,12.6,1.0))
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('twoDice.png')
pylab.show()

Could anyone help me how to plot cdf?

Answer 1

You could directly use the histogram plotting function to achieve that, e.g.

import pylab
import random
import numpy as np

sampleSize = 100


## Let's simulate the repeated throwing of a single six-sided die
singleDie = []
for i in range(sampleSize):
    newValue = random.randint(1,6)
    singleDie.append(newValue)

print "Results for throwing a single die", sampleSize, "times."
print "Mean of the sample =", pylab.mean(singleDie)
print "Median of the sample =", pylab.median(singleDie)
print "Standard deviation of the sample =", pylab.std(singleDie)


pylab.hist(singleDie, bins=[0.5,1.5,2.5,3.5,4.5,5.5,6.5] )
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('singleDie.png')
pylab.show()

## What about repeatedly throwing two dice and summing them?
twoDice = []
for i in range(sampleSize):
    newValue = random.randint(1,6) + random.randint(1,6)
    twoDice.append(newValue)

print "Results for throwing two dices", sampleSize, "times."
print "Mean of the sample =", pylab.mean(twoDice)
print "Median of the sample =", pylab.median(twoDice)
#print "Standard deviation of the sample =", pylab.std(twoDice)

pylab.hist(twoDice, bins= pylab.arange(1.5,12.6,1.0))
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('twoDice.png')
pylab.show()

pylab.hist(twoDice, bins=pylab.arange(1.5,12.6,1.0), normed=1, histtype='step', cumulative=True)
pylab.xlabel('Value')
pylab.ylabel('Fraction')
pylab.show()

Notice the new line:

pylab.hist(twoDice, bins=pylab.arange(1.5,12.6,1.0), normed=1, histtype='step', cumulative=True)

which should give directly the cdf plot. If you don't specify normed=1 you will see the scale (0-100) which will represent percentages instead of the usual probability scale (0-1).

There are also other ways to do it. For example:

import pylab
import random
import numpy as np

sampleSize = 100


## Let's simulate the repeated throwing of a single six-sided die
singleDie = []
for i in range(sampleSize):
    newValue = random.randint(1,6)
    singleDie.append(newValue)

print "Results for throwing a single die", sampleSize, "times."
print "Mean of the sample =", pylab.mean(singleDie)
print "Median of the sample =", pylab.median(singleDie)
print "Standard deviation of the sample =", pylab.std(singleDie)


pylab.hist(singleDie, bins=[0.5,1.5,2.5,3.5,4.5,5.5,6.5] )
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('singleDie.png')
pylab.show()

## What about repeatedly throwing two dice and summing them?
twoDice = []
for i in range(sampleSize):
    newValue = random.randint(1,6) + random.randint(1,6)
    twoDice.append(newValue)

print "Results for throwing two dices", sampleSize, "times."
print "Mean of the sample =", pylab.mean(twoDice)
print "Median of the sample =", pylab.median(twoDice)
#print "Standard deviation of the sample =", pylab.std(twoDice)

pylab.hist(twoDice, bins= pylab.arange(1.5,12.6,1.0))
pylab.xlabel('Value')
pylab.ylabel('Count')
pylab.savefig('twoDice.png')
pylab.show()

twod_cdf = np.array(twoDice)

X_values = np.sort(twod_cdf)
F_values = np.array(range(sampleSize))/float(sampleSize)
pylab.plot(X_values, F_values)
pylab.xlabel('Value')
pylab.ylabel('Fraction')
pylab.show()

Notice now that we sort the array, build the function and plot it.