如何在 python 中为六面骰子模拟绘制累积分布函数？

Question

我正在尝试

1. 用模拟的骰子和结果的频率绘制直方图。
2. 计算并绘制累积分布函数。
3. 查找并绘制中位数。

到目前为止，这是我所拥有的：

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()

谁能帮助我如何绘制 cdf？

Answer 1

您可以直接使用直方图绘图功能来实现，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 normed=1，您将看到表示百分比的比例 (0-100)，而不是通常的概率比例 (0-1)。

还有其他方法可以做到这一点。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()

现在请注意，我们对数组进行排序、构建函数并绘制它。