def _MixPmf(suite):
high = 10
metapmf = thinkbayes.Pmf()
for lam, prob in suite.Items():
pmf = thinkbayes.MakePoissonPmf(lam, high, step=1)
metapmf.Set(pmf, y=prob)
return thinkbayes.MakeMixture(metapmf, name='mix')
def CH7_2():
"""
http://www.ruanyifeng.com/blog/2015/06/poisson-distribution.html
1. 一场比赛平均进球数为lam, 每场比赛进球分布: 泊松分布
(进球可以在任何时间点发生)
eg. 某医院平均每小时出生3个婴儿
重点是: 次数
2. 进球间隔的分布: 指数分布
eg. 某医院婴儿出生的时间间隔(20分钟一个(0.3h))
重点是: 间隔
泊松分布是单位时间内独立事件发生次数的概率分布
指数分布是独立事件的时间间隔的概率分布
"""
# 单位时间内出生1 - 10个婴儿的泊松分布
pmf = thinkbayes.MakePoissonPmf(3, 10, step=1)
thinkplot.Clf()
thinkplot.Pmf(pmf)
# thinkplot.Show();
# 婴儿出生时间间隔(20分钟)
pmf = thinkbayes.MakeExponentialPmf(0.3, 10, n=200)
thinkplot.Clf()
thinkplot.Pmf(pmf)
thinkplot.Show();
def CH7_4(show = 1):
"""
混合分布
"""
suite1, suite2 = CH7_3(0)
# 均值:
mu1 = suite1.Mean()
mu2 = suite2.Mean()
print("Mean1: ", mu1)
print("Mean2: ", mu2)
if show:
# 使用均值, 计算泊松分布 (下一场比赛进球分布)
pos1 = thinkbayes.MakePoissonPmf(mu1, 10, step=1)
pos2 = thinkbayes.MakePoissonPmf(mu2, 10, step=1)
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmfs([pos1, pos2])
thinkplot.Show(title='Poisson', xlabel='Goals per game', ylabel='Probability')
# 混合分布
def _MixPmf(suite):
high = 10
metapmf = thinkbayes.Pmf()
for lam, prob in suite.Items():
pmf = thinkbayes.MakePoissonPmf(lam, high, step=1)
metapmf.Set(pmf, y=prob)
return thinkbayes.MakeMixture(metapmf, name='mix')
mix1 = _MixPmf(suite1)
mix2 = _MixPmf(suite2)
if show:
thinkplot.Clf()
thinkplot.PrePlot(num=2)
thinkplot.Pmfs([mix1, mix2])
thinkplot.Show(title='Mixture', xlabel='Goals per game', ylabel='Probability')
return mix1, mix2
def __init__(self, r, f, high=500, step=5):
"""Initializes the suite.
r: known emission rate, r
f: fraction of particles registered
high: maximum number of particles, n
step: step size between hypothetical values of n
"""
pmf = thinkbayes.MakePoissonPmf(r, high, step=step)
thinkbayes.Suite.__init__(self, pmf, name=r)
self.r = r
self.f = f
def MakeGoalPmf(suite, high=10):
"""Makes the distribution of goals scored, given distribution of lam.
suite: distribution of goal-scoring rate
high: upper bound
returns: Pmf of goals per game
"""
metapmf = thinkbayes.Pmf()
for lam, prob in suite.Items():
pmf = thinkbayes.MakePoissonPmf(lam, high)
metapmf.Set(pmf, prob)
mix = thinkbayes.MakeMixture(metapmf, name=suite.name)
return mix