def main():
df = hinc.ReadData()
log_sample = InterpolateSample(df, log_upper=6.0)
log_cdf = thinkstats2.Cdf(log_sample)
print("median", thinkstats2.Median(log_sample))
print("pearson's median skewness",
thinkstats2.PearsonMedianSkewness(log_sample))
print("skewness", thinkstats2.Skewness(log_sample))
print("mean", log_cdf.Mean())
print(
"the higher our log_upper, the more right-skewed (according to g_1) or at least less left-skewed (according to g_p) things get"
)
print("the mean moves to the right a bit, too.")
print("proportion of the population with income < mean",
log_cdf.Prob(log_cdf.Mean()))
print(
"the higher the upper bound, the greater the proprtion below the mean."
)
thinkplot.Cdf(log_cdf)
thinkplot.Show(xlabel='household income', ylabel='CDF')
def PearsonMedianSkewness(xs):
median = thinkstats2.Median(xs)
mean = RawMoment(xs, 1)
var = CentralMoment(xs, 2)
std = math.sqrt(var)
gp = 3 * (mean - median) / std
return gp
def Summarize(data):
mean = data.mean()
std = data.std()
median = thinkstats2.Median(data)
print('mean', mean)
print('std', std)
print('median', median)
print('skewness', thinkstats2.Skewness(data))
print('pearson skewness', thinkstats2.PearsonMedianSkewness(data))
return mean, median
def Summarize(data):
"""Prints summary statistics.
data: pandas Series
"""
mean = data.mean()
std = data.std()
median = thinkstats2.Median(data)
print('mean', mean)
print('std', std)
print('median', median)
print('skewness', thinkstats2.Skewness(data))
print('pearson skewness', thinkstats2.PearsonMedianSkewness(data))
return mean, median
def Experiment1(n=6, m=1000):
mu = 0
sigma = 1
means = []
medians = []
for _ in range(m):
xs = [random.gauss(mu, sigma) for i in range(n)]
xbar = numpy.mean(xs)
median = thinkstats2.Median(xs)
means.append(xbar)
medians.append(median)
print 'rmse xbar', RMSE(means, mu)
print 'rmse median', RMSE(medians, mu)
def Experiment3(n=7, m=1000):
lam = 2
means = []
medians = []
for _ in range(m):
xs = [random.expovariate(lam) for i in range(n)]
L = 1 / numpy.mean(xs)
Lm = math.log(2) / thinkstats2.Median(xs)
means.append(L)
medians.append(Lm)
print 'rmse L', RMSE(means, lam)
print 'rmse Lm', RMSE(medians, lam)
print 'mean error L', MeanError(means, lam)
print 'mean error Lm', MeanError(medians, lam)
def describe_inc_dist(log_upper):
log_sample = hinc2.InterpolateSample(df, log_upper=j)
incomes = np.power(10, log_sample)
inc_mean = thinkstats2.Mean(incomes)
inc_med = thinkstats2.Median(incomes)
inc_skew = thinkstats2.Skewness(incomes)
inc_pearskew = thinkstats2.PearsonMedianSkewness(incomes)
print('log_upper = ', j)
print('Mean Income: ', inc_mean)
print('Median Income: ', inc_med)
print('Skewness: ', inc_skew)
print('Pearson Median Skewness: ', inc_pearskew)
cdf = thinkstats2.Cdf(incomes)
inc_below_mean = cdf.Prob(inc_mean)
print('Pct. below mean: ', inc_below_mean)
print('\n')
def SimulateSampleExpo(lam=2.0, n=10, iters=1000):
"""Simulate samples of exponential dist of lambda 'lam'
of size 'n' for 'm' iters.
lam: float shape parameter
n: sample size
iters: number of iterations
return:
Ls - estimates of lam based on mean
Lms - estimates of lam based on median
"""
Ls = []
Lms = []
for j in range(iters):
xs = np.random.exponential(1.0 / lam, n)
L = 1 / np.mean(xs)
Lm = np.log(2) / thinkstats2.Median(xs)
Ls.append(L)
Lms.append(Lm)
return Ls, Lms
def Estimate3(n=7, iters=1000):
"""Evaulates sample mean and sample median as estimators for properties of
exponential distribution.
n: int sample size
iters: int number of iterations
return: None
"""
lam = 2
means = []
medians = []
for _ in range(iters):
xs = np.random.exponential(1.0 / lam, n)
L = 1 / np.mean(xs)
Lm = np.log(2) / thinkstats2.Median(xs)
means.append(L)
medians.append(Lm)
print('RMSE(means, lam):\n', RMSE(means, lam))
print('RMSE(medians, lam):\n', RMSE(medians, lam))
print('MeanError(means, lam):\n', MeanError(means, lam))
print('MeanError(medians, lam):\n', MeanError(medians, lam))
for n in n_arr:
lams = SimulateSample(lam, n, 1000)
SampleDistrPLot(lams, n, lam)
thinkplot.Config(xlabel='L estimate',
ylabel='CDF',
title='Sampling distribution',
xlim=[0, 4],
legend=True)
#--- Chapter6 Ex1
df = hinc.ReadData()
log_sample = hinc2.InterpolateSample(df, log_upper=6.0)
sample = np.power(10, log_sample)
print('Mean = ', sample.mean())
print('Median =', thinkstats2.Median(sample))
print('Skewness =', thinkstats2.Skewness(sample))
print('Pearson Median Skweness =', thinkstats2.PearsonMedianSkewness(sample))
income_cdf = thinkstats2.Cdf(sample)
print(income_cdf.Prob(sample.mean()) * 100)
#--- Chapter8 Ex3
def SimulateGame(lam):
t = 0
goals = 0
while True:
time_int = random.expovariate(lam)
t += time_int
if t > 1:
break
greq = preg[preg.agepreg >= 30]
less = preg[preg.agepreg < 30]
assert len(greq) == 2635
assert len(less) == 10606
return greq, less
def MakePdfs(greq, less):
greqpdf = thinkstats2.EstimatedPdf(greq.totalwgt_lb.dropna())
lesspdf = thinkstats2.EstimatedPdf(less.totalwgt_lb.dropna())
thinkplot.PrePlot(rows=1, cols=2)
thinkplot.SubPlot(1)
thinkplot.Pdf(greqpdf, label='greater/equal to 30')
thinkplot.Config(xlabel='Birth weight (lbs)', ylabel='PDF')
thinkplot.SubPlot(2)
thinkplot.Pdf(lesspdf, label='less than 30')
thinkplot.Config(xlabel='Birth weight (lbs)', ylabel='PDF')
thinkplot.Show()
greq, less = MakeFrames()
MakePdfs(greq, less)
print "greater/equal to 30 skew:", thinkstats2.Skewness(greq.totalwgt_lb.dropna())
print "less than 30 skew:", thinkstats2.Skewness(less.totalwgt_lb.dropna())
print "greater/equal to 30 mean:", thinkstats2.Mean(greq.totalwgt_lb.dropna())
print "greater/equal to 30 median:", thinkstats2.Median(greq.totalwgt_lb.dropna())
print "less than 30 mean:", thinkstats2.Mean(less.totalwgt_lb.dropna())
print "less than 30 median:", thinkstats2.Median(less.totalwgt_lb.dropna())
