def CH5_4():
"""
加法操作:
转动3个6面的骰子, 计算它们的和, 采用下面两种方式, 对比分布图.
模拟:
通过模拟随机样品, 累积和.
枚举:
枚举所有可能的数字对
"""
d6 = Die(6)
k = 3
print("mean(d6) = %.3f, sum(probs) = %.3f" % (d6.Mean(), d6.Total()))
# 模拟: 3个骰子分布, N越大越精确. 缺点: 耗时.
N = 1000
dists = [d6] * k
pmf = thinkbayes.SampleSum(dists, N)
pmf.name = 'sim'
thinkplot.Pmf(pmf)
print("mean([d6]*3) = %.3f, sum(*) = %.3f" % (pmf.Mean(), pmf.Total()))
# 枚举: x数值相加, y概率相乘
pmf = d6 + d6 + d6
pmf.name = 'enum'
thinkplot.Pmf(pmf)
thinkplot.Show(xlabel='sum([d6]*3)', ylabel='probablity')
print("mean([d6]*3) = %.3f, sum(*) = %.3f" % (pmf.Mean(), pmf.Total()))
def main():
d6 = Die(6)
dice = [d6] * 3
three = thinkbayes.SampleSum(dice, 1000)
print(three.Items())
thinkplot.PrePlot(1)
thinkplot.Pmf(three)
thinkplot.Save(root='dice_self1',
xlabel='sum of dice',
ylabel='Probability',
formats=['pdf'])
def main():
pmf_dice = thinkbayes.Pmf()
pmf_dice.Set(Die(4), 5)
pmf_dice.Set(Die(6), 4)
pmf_dice.Set(Die(8), 3)
pmf_dice.Set(Die(12), 2)
pmf_dice.Set(Die(20), 1)
pmf_dice.Normalize()
mix = thinkbayes.Pmf()
for die, weight in pmf_dice.Items():
for outcome, prob in die.Items():
mix.Incr(outcome, weight * prob)
mix = thinkbayes.MakeMixture(pmf_dice)
colors = thinkplot.Brewer.Colors()
thinkplot.Hist(mix, width=0.9, color=colors[4])
thinkplot.Save(root='dungeons3',
xlabel='Outcome',
ylabel='Probability',
formats=FORMATS)
random.seed(17)
d6 = Die(6, 'd6')
dice = [d6] * 3
three = thinkbayes.SampleSum(dice, 1000)
three.name = 'sample'
three.Print()
three_exact = d6 + d6 + d6
three_exact.name = 'exact'
three_exact.Print()
thinkplot.PrePlot(num=2)
thinkplot.Pmf(three)
thinkplot.Pmf(three_exact, linestyle='dashed')
thinkplot.Save(root='dungeons1',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.15],
formats=FORMATS)
thinkplot.Clf()
thinkplot.PrePlot(num=1)
# compute the distribution of the best attribute the hard way
# best_attr2 = PmfMax(three_exact, three_exact)
# best_attr4 = PmfMax(best_attr2, best_attr2)
# best_attr6 = PmfMax(best_attr4, best_attr2)
# thinkplot.Pmf(best_attr6)
# and the easy way
best_attr_cdf = three_exact.Max(6)
best_attr_cdf.name = ''
best_attr_pmf = thinkbayes.MakePmfFromCdf(best_attr_cdf)
best_attr_pmf.Print()
thinkplot.Pmf(best_attr_pmf)
thinkplot.Save(root='dungeons2',
xlabel='Sum of three d6',
ylabel='Probability',
axis=[2, 19, 0, 0.23],
formats=FORMATS)