如何在Python中绘制六面骰子模拟的累积分布函数

Question

我正在尝试

1. 绘制直方图具有模拟中的骰子和结果频率。
2. 计算和绘制累积分布函数。
3. 找到并绘制中间。

到目前为止，这就是我所拥有的：

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()

谁能帮我如何绘制CDF？

Answer 1

您可以直接使用直方图绘图函数来实现这一目标，例如

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()

注意新行：

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

应该直接给出CDF图。如果您不指定标准= 1，则会看到比例尺（0-100），该比例表示百分比，而不是通常的概率量表（0-1）。

还有其他方法可以做到。例如：

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()

请注意，现在我们对数组进行排序，构建功能并绘制它。