def Render(self):
"""Returns pair of xs, ys suitable for plotting.
"""
mean, std = self.mu, self.sigma
low, high = mean - 3 * std, mean + 3 * std
xs, ys = thinkstats2.RenderNormalCdf(mean, std, low, high)
return xs, ys
def MakeNormalModel(arrivalDelays):
"""Plot the CDF of arrival delays with a normal model.
This is a modified copy from analytic.py
"""
# estimate parameters: trimming outliers yields a better fit
mu, var = thinkstats2.TrimmedMeanVar(arrivalDelays, p=0.01)
print('Mean, Var', mu, var)
# plot the model
sigma = math.sqrt(var)
print('Sigma', sigma)
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=12.5)
thinkplot.Plot(xs, ps, label='model', color='0.8')
# plot the data
cdf = thinkstats2.Cdf(arrivalDelays, label='data')
thinkplot.PrePlot(1)
thinkplot.Cdf(cdf)
thinkplot.Save(root='NormalModel_arrivaldelay_model',
title='Arrival Delays',
xlabel='arrival delays (min)',
ylabel='CDF')
def PlotNormalModel(sample, title="", xlabel=""):
cdf = thinkstats2.Cdf(sample, label="actual")
mu, var = thinkstats2.TrimmedMeanVar(sample, p=0.01)
sigma = np.sqrt(var)
xmin = mu - 4.0 * sigma
xmax = mu + 4.0 * sigma
xs, ys = thinkstats2.RenderNormalCdf(mu, sigma, xmin, xmax)
thinkplot.Cdf(cdf)
thinkplot.plot(xs,
ys,
label=r'model $\mu$={:.2f} $\sigma$={:.2f}'.format(
mu, sigma))
thinkplot.Config(title=title, xlabel=xlabel, ylabel="CDF")
def MakeNormalModel(data, label):
cdf = thinkstats2.Cdf(data, label=label)
mean, var = thinkstats2.TrimmedMeanVar(data)
std = np.sqrt(var)
print('n, mean, std', len(data), mean, std)
xmin = mean - 4 * std
xmax = mean + 4 * std
xs, ps = thinkstats2.RenderNormalCdf(mean, std, xmin, xmax)
thinkplot.Plot(xs, ps, label='model', linewidth=4, color='0.8')
thinkplot.Cdf(cdf)
def MakeFigures():
"""Plots the CDF of populations in several forms.
On a log-log scale the tail of the CCDF looks like a straight line,
which suggests a Pareto distribution, but that turns out to be misleading.
On a log-x scale the distribution has the characteristic sigmoid of
a lognormal distribution.
The normal probability plot of log(sizes) confirms that the data fit the
lognormal model very well.
Many phenomena that have been described with Pareto models can be described
as well, or better, with lognormal models.
"""
pops = ReadData()
print('Number of cities/towns', len(pops))
log_pops = np.log10(pops)
cdf = thinkstats2.Cdf(pops, label='data')
cdf_log = thinkstats2.Cdf(log_pops, label='data')
# pareto plot
xs, ys = thinkstats2.RenderParetoCdf(xmin=5000, alpha=1.4, low=0, high=1e7)
thinkplot.Plot(np.log10(xs), 1-ys, label='model', color='0.8')
thinkplot.Cdf(cdf_log, complement=True)
thinkplot.Config(xlabel='log10 population',
ylabel='CCDF',
yscale='log')
thinkplot.Save(root='populations_pareto')
# lognormal plot
thinkplot.PrePlot(cols=2)
mu, sigma = log_pops.mean(), log_pops.std()
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=8)
thinkplot.Plot(xs, ps, label='model', color='0.8')
thinkplot.Cdf(cdf_log)
thinkplot.Config(xlabel='log10 population',
ylabel='CDF')
thinkplot.SubPlot(2)
thinkstats2.NormalProbabilityPlot(log_pops, label='data')
thinkplot.Config(xlabel='z',
ylabel='log10 population',
xlim=[-5, 5])
thinkplot.Save(root='populations_normal')
def MakeNormalModel(weights):
"""Plots a CDF with a Normal model.
weights: sequence
"""
cdf = thinkstats2.Cdf(weights, label='weights')
mean, var = thinkstats2.TrimmedMeanVar(weights)
std = math.sqrt(var)
print('n, mean, std', len(weights), mean, std)
xmin = mean - 4 * std
xmax = mean + 4 * std
xs, ps = thinkstats2.RenderNormalCdf(mean, std, xmin, xmax)
thinkplot.Plot(xs, ps, label='model', linewidth=4, color='0.8')
thinkplot.Cdf(cdf)
def MakeNormalModel(age):
"""Plots a CDF with a Normal model.
age: sequence
"""
cdf = thinkstats2.Cdf(age, label='variable')
mean, var = thinkstats2.TrimmedMeanVar(age)
std = np.sqrt(var)
print('n, mean, std', len(age), mean, std)
xmin = mean - 4 * std
xmax = mean + 4 * std
xs, ps = thinkstats2.RenderNormalCdf(mean, std, xmin, xmax)
thinkplot.Plot(xs, ps, label='model', linewidth=4, color='0.8')
thinkplot.Cdf(cdf)
def MakeNormalCdf():
"""Generates a plot of the normal CDF."""
thinkplot.PrePlot(3)
mus = [1.0, 2.0, 3.0]
sigmas = [0.5, 0.4, 0.3]
for mu, sigma in zip(mus, sigmas):
xs, ps = thinkstats2.RenderNormalCdf(mu=mu, sigma=sigma,
low=-1.0, high=4.0)
label = r'$\mu=%g$, $\sigma=%g$' % (mu, sigma)
thinkplot.Plot(xs, ps, label=label)
thinkplot.Save(root='analytic_normal_cdf',
title='Normal CDF',
xlabel='x',
ylabel='CDF',
loc=2)
def MakeFigures(df):
"""Plots the CDF of income in several forms.
"""
xs, ps = df.income.values, df.ps.values
cdf = SmoothCdf(xs, ps, label='data')
cdf_log = SmoothCdf(np.log10(xs), ps, label='data')
# linear plot
thinkplot.Cdf(cdf)
thinkplot.Save(root='hinc_linear', xlabel='household income', ylabel='CDF')
# pareto plot
# for the model I chose parameters by hand to fit the tail
xs, ys = thinkstats2.RenderParetoCdf(xmin=55000,
alpha=2.5,
low=0,
high=250000)
thinkplot.Plot(xs, 1 - ys, label='model', color='0.8')
thinkplot.Cdf(cdf, complement=True)
thinkplot.Save(root='hinc_pareto',
xlabel='log10 household income',
ylabel='CCDF',
xscale='log',
yscale='log')
# lognormal plot
# for the model I estimate mu and sigma using
# percentile-based statistics
median = cdf_log.Percentile(50)
iqr = cdf_log.Percentile(75) - cdf_log.Percentile(25)
std = iqr / 1.349
# choose std to match the upper tail
std = 0.35
print(median, std)
xs, ps = thinkstats2.RenderNormalCdf(median, std, low=3.5, high=5.5)
thinkplot.Plot(xs, ps, label='model', color='0.8')
thinkplot.Cdf(cdf_log)
thinkplot.Save(root='hinc_normal',
xlabel='log10 household income',
ylabel='CDF')
def MakeNormalModel(weights):
"""Plot the CDF of birthweights with a normal model."""
# estimate parameters: trimming outliers yields a better fit
mu, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)
print('Mean, Var', mu, var)
# plot the model
sigma = math.sqrt(var)
print('Sigma', sigma)
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=12.5)
thinkplot.Plot(xs, ps, label='model', color='0.8')
# plot the data
cdf = thinkstats2.Cdf(weights, label='data')
thinkplot.PrePlot(1)
thinkplot.Cdf(cdf)
thinkplot.Save(root='analytic_birthwgt_model',
title='Birth weights',
xlabel='birth weight (lbs)',
ylabel='CDF')
thinkplot.Cdf(cdf)
thinkplot.Show(xlabel='Parts per Million', ylabel='CDF')
#plotting a complementary CDF (CCDF) of O3
thinkplot.Cdf(cdf, complement=True)
thinkplot.Show(xlabel='minutes', ylabel='CCDF', yscale='log')
#normal CDF with a range of parameters
thinkplot.PrePlot(3)
mus = [1.0, 2.0, 3.0] #should change to my own numbers instead
sigmas = [0.5, 0.4, 0.3]
for mu, sigma in zip(mus, sigmas):
xs, ps = thinkstats2.RenderNormalCdf(mu=mu,
sigma=sigma,
low=-1.0,
high=4.0)
label = r'$\mu=%g$, $\sigma=%g$' % (mu, sigma)
thinkplot.Plot(xs, ps, label=label)
thinkplot.Config(title='Normal CDF',
xlabel='x',
ylabel='CDF',
loc='upper left')
thinkplot.Show()
#Scatterplots
thinkplot.Scatter(grp_pollution_df['NO2AQI'],
grp_pollution_df['SO2AQI'],
alpha=1)
thinkplot.Config(xlabel='NO2 & SO2 AQI',
yscale='log',
loc='upper right')
#%% [markdown]
# ## Normal distribution
#
# Here's what the normal CDF looks like with a range of parameters.
#%%
thinkplot.PrePlot(3)
mus = [1.0, 2.0, 3.0]
sigmas = [0.5, 0.4, 0.3]
for mu, sigma in zip(mus, sigmas):
xs, ps = thinkstats2.RenderNormalCdf(mu=mu,
sigma=sigma,
low=-1.0,
high=4.0)
label = r'$\mu=%g$, $\sigma=%g$' % (mu, sigma)
thinkplot.Plot(xs, ps, label=label)
thinkplot.Config(title='Normal CDF',
xlabel='x',
ylabel='CDF',
loc='upper left')
#%% [markdown]
# I'll use a normal model to fit the distribution of birth weights from the NSFG.
#%%
preg = nsfg.ReadFemPreg()
weights = preg.totalwgt_lb.dropna()
thinkplot.Cdf(log_cdf, complement=True)
xmin = 5000
alpha = 1.4
xs, ys = thinkstats2.RenderParetoCdf(xmin=xmin, alpha=alpha, low=0, high=1.0e7)
thinkplot.Plot(np.log10(xs),
1 - ys,
label=r'model $x_m={}$ $\alpha={}$'.format(xmin, alpha))
thinkplot.Config(yscale='log', xlabel='log10 pupulation', ylabel='CCDF')
#%%
thinkplot.Cdf(log_cdf)
mu, var = thinkstats2.TrimmedMeanVar(log_pops, p=0.01)
sigma = np.sqrt(var)
xmin = mu - 4.0 * sigma
xmax = mu + 4.0 * sigma
xs, ys = thinkstats2.RenderNormalCdf(mu, sigma, xmin, xmax)
thinkplot.plot(xs,
ys,
label=r'model $\mu$={:.2f} $\sigma$={:.2f}'.format(mu, sigma))
thinkplot.Config(xlabel='log10 pupulation', ylabel='CDF')
#%%
PlotNormalProbability(log_pops, ylabel="log10 population")
#%% [markdown]
# ## 5.6 random
#%%
import math
max(filmsdata.budget)
# In[444]:
min(filmsdata.budget)
# In[445]:
# plot the model
sigma = np.sqrt(var)
print('Sigma', sigma)
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=7000, high=380000000)
thinkplot.Plot(xs, ps, label='model', color='0.6')
cdf = thinkstats2.Cdf(filmsdata.budget, label='data')
thinkplot.PrePlot(1)
thinkplot.Cdf(cdf)
thinkplot.Config(title='Film Budgets Normal Distribution',
xlabel='Film Budgets',
ylabel='CDF')
# Next, I will observe the relationship between profit and budget. I will begin by plotting a scatterplot of these two variables.
# In[446]:
def CDFVisualDist(cdf):
xs, ps = cdf.xs, cdf.ps
# set up subplots
PrePlot(num=6, cols=3, rows=2)
# linear plot
SubPlot(1)
Cdf(cdf, color='C0')
Config(xlabel='x', ylabel='CDF', title='Linear Plot')
# lognormal plot
SubPlot(2)
xs_log = np.log10(xs)
cdf_log = thinkstats2.Cdf(xs_log, ps, label='data')
median = cdf_log.Percentile(50)
iqr = thinkstats2.IQRFromCDF(cdf_log)
std = thinkstats2.StdFromIQR(iqr)
low = np.nanmin(xs_log[xs_log != -np.inf])
high = np.nanmax(xs_log[xs_log != np.inf])
x_norm, p_norm = thinkstats2.RenderNormalCdf(median,
std,
low=low,
high=high)
Plot(x_norm, p_norm, label='model', color='0.8')
Cdf(cdf_log, color='C0')
Config(xlabel='log10 x', ylabel='CDF', title='Lognormal Plot')
# pareto plot
SubPlot(3)
scale = Cdf(cdf, transform='pareto', color='C0')
Config(xlabel='x', ylabel='CCDF', title='Pareto Plot', **scale)
# exponential plot
SubPlot(4)
mean = cdf.NaNMean()
lam = 1 / mean
low = np.nanmin(xs[xs != -np.inf])
high = np.nanmax(xs[xs != np.inf])
expo_xs, expo_ps = thinkstats2.RenderExpoCdf(lam, low, high)
Plot(expo_xs, 1 - expo_ps, label='model', color='0.8')
scale = Cdf(cdf, transform='exponential', color='C0')
Config(xlabel='x', ylabel='CCDF', title='Exponential Plot', **scale)
# normal plot
SubPlot(5)
var = cdf.NaNVar()
std = np.sqrt(var)
low = mean - 4 * std
high = mean + 4 * std
norm_xs, norm_ps = thinkstats2.RenderNormalCdf(mean, std, low, high)
Cdf(cdf, color='C0')
Plot(norm_xs, norm_ps, label='model', linewidth=4, color='0.8')
Config(xlabel='x', ylabel='CDF', title='Normal Plot')
# weibull plot
SubPlot(6)
scale = Cdf(cdf, transform='weibull', color='C0')
Config(title='weibull transform',
xlabel='log x',
ylabel='log log CCDF',
**scale)
Show()
