def testIntelligenceScale():
"""
通过erf.NormalCdf()得到正太分布的近似累积分布
"""
"""
eg: 正态分布(μ=100, σ=15) 用erf.NormalCdf 函数查看正态分布中罕见事件的频数。
高于均值, 115、130、145 的分别是多少(百分比)?
"""
mu, sigma = 100, 15
IQs = [mu, 115, 130, 145]
ys = []
for iq in IQs:
percent = (1 - erf.NormalCdf(iq, mu=mu, sigma=sigma)) * 100
ys.append(percent)
print("%.2f%% people IQ > %d" % (percent, iq))
plt.bar(IQs, ys, width=0.8, align="center")
plt.show()
"""
六西格玛: 超出均值6个标准差的值, 100 + 6 * 15 = 190
"""
people = 6 * 1000 * 1000 * 1000 * (1 - erf.NormalCdf(mu + 6*sigma, mu=mu, sigma=sigma))
print("%d people IQ > %d" % (people, 5*sigma))
pass
def process(data):
# Hist 分布图
hist = Pmf.MakeHistFromList(data, name='hist')
myplot.Hist(hist, color='blue')
myplot.Show()
# Pmf 分布图
pmf = Pmf.MakePmfFromHist(hist, name='pmf')
myplot.Pmf(pmf, color='yellow')
myplot.Show()
myplot.Clf()
# 实际数据的CDF分布图
cdf = Cdf.MakeCdfFromList(data, name='loafs')
myplot.Cdf(cdf)
mu, var = thinkstats.MeanVar(data)
sigma = math.sqrt(var)
print("mu = %.3f, sigma = %.3f" % (mu, sigma))
# 正态分布
xs = normal_sample(len(data), mu, sigma) # xs = data
ys = [erf.NormalCdf(x, mu=mu, sigma=sigma) for x in xs]
myplot.Scatter(xs, ys, color='red', label='sample')
myplot.Show()
def Test(actual1, actual2, model, iters=1000):
"""Estimates p-values based on differences in the mean.
Args:
actual1:
actual2: sequences of observed values for groups 1 and 2
model: sequences of values from the hypothetical distribution
"""
n = len(actual1)
m = len(actual2)
# compute delta
mu1, mu2, delta = hypothesis.DifferenceInMean(actual1, actual2)
delta = abs(delta)
print('n:', n)
print('m:', m)
print('mu1', mu1)
print('mu2', mu2)
print('delta', delta)
# compute the expected distribution of differences in sample mean
mu_pooled, var_pooled = thinkstats.MeanVar(model)
print('(Mean, Var) of pooled data', mu_pooled, var_pooled)
f = 1.0 / n + 1.0 / m
mu, var = (0, f * var_pooled)
print('Expected Mean, Var of deltas', mu, var)
# compute the p-value of delta in the observed distribution
sigma = math.sqrt(var)
left = erf.NormalCdf(-delta, mu, sigma)
right = 1 - erf.NormalCdf(delta, mu, sigma)
pvalue = left + right
print('Tails:', left, right)
print('p-value:', pvalue)
# compare the mean and variance of resamples differences
deltas = [hypothesis.Resample(model, model, n, m) for i in range(iters)]
mean_var = thinkstats.MeanVar(deltas)
print('(Mean, Var) of resampled deltas', mean_var)
return pvalue
def CmpNormalModelWithDataSample():
firsts, others, babies = Babies.PartitionBabies()
weights = Babies.GetWightList(babies)
pmf = Pmf.MakePmfFromList(weights)
mu = pmf.Mean()
var = pmf.Var(mu)
sigma = math.sqrt(var)
print("mu = {}, var = {}, sigma = {}".format(mu, var, sigma))
# 经验分布, 数据
cdf = Cdf.MakeCdfFromPmf(pmf, name='data')
myplot.cdf(cdf)
# u, sigma --> 误差函数计算 模型
xs, yy = pmf.Render()
ys = [erf.NormalCdf(x, mu, sigma) for x in xs]
myplot.Plot(xs, ys, label='Model')
myplot.Show()
myplot.Clf()
#!/usr/bin/python3
# -*- coding: utf-8 -*-
import math
import Babies
import Cdf
import myplot
import thinkstats
import erf
if __name__ == "__main__":
firsts, others, babies = Babies.PartitionBabies()
preglengths = Babies.GetPregnacyList(babies)
mu = thinkstats.Mean(preglengths)
sigma = math.sqrt(thinkstats.Var(preglengths, mu))
print("mu = %.3f sigma = %.3f" % (mu, sigma))
cdf0 = Cdf.MakeCdfFromList(preglengths, name='cdf0')
ys = [erf.NormalCdf(x, mu=mu, sigma=sigma) for x in preglengths]
cdf1 = Cdf.Cdf(preglengths, ys, 'cdf1')
myplot.Cdf(cdf1, complement=False, transform=None)
myplot.Cdfs([cdf0, cdf1], complement=False, transform=None)
myplot.Show()
# TODO wrong
def main():
x = range(200)
cdf = [erf.NormalCdf(_x,mu=100,sigma=15) for _x in x]
print('{:.3f} of people have more than 190IQ '.format((1-cdf[189])*6*(10)**9))
plt.plot(x, cdf)
plt.show()
def RenderNormalCdf(mu, sigma, max, n=50):
"""Generates sequences of xs and ps for a normal CDF."""
xs = [max * i / n for i in range(n)]
ps = [erf.NormalCdf(x, mu, sigma) for x in xs]
return xs, ps
def underNormal(value, m, s):
return erf.NormalCdf(value, mu=m, sigma=s)
def overNormal(value, m, s):
return 1 - erf.NormalCdf(value, mu=m, sigma=s)