def MakeExpoCdf():
"""Generates a plot of the exponential CDF."""
thinkplot.PrePlot(3)
for lam in [2.0, 1, 0.5]:
xs, ps = thinkstats2.RenderExpoCdf(lam, 0, 3.0, 50)
thinkplot.Plot(xs, ps, label='lam=%g' % lam)
thinkplot.Save(root='analytic_expo_cdf',
title='Exponential CDF',
xlabel='x',
ylabel='CDF')
import nsfg
import first
import analytic
import thinkstats2
import thinkplot
#%% [markdown]
# ## Exponential distribution
#
# Here's what the exponential CDF looks like with a range of parameters.
#%%
thinkplot.PrePlot(3)
for lam in [2.0, 1, 0.5]:
xs, ps = thinkstats2.RenderExpoCdf(lam, 0, 3.0, 50)
label = r'$\lambda=%g$' % lam
thinkplot.Plot(xs, ps, label=label)
thinkplot.Config(title='Exponential CDF',
xlabel='x',
ylabel='CDF',
loc='lower right')
#%% [markdown]
# Here's the distribution of interarrival times from a dataset of birth times.
#%%
df = analytic.ReadBabyBoom()
diffs = df.minutes.diff()
cdf = thinkstats2.Cdf(diffs, label='actual')
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()