def testNormalPdf(self):
pdf = thinkstats2.NormalPdf(mu=1, sigma=2)
self.assertEqual(len(str(pdf)), 29)
self.assertAlmostEqual(pdf.Density(3), 0.12098536226)
pmf = pdf.MakePmf()
self.assertAlmostEqual(pmf[1.0], 0.0239951295619)
xs, ps = pdf.Render()
self.assertEqual(xs[0], -5.0)
self.assertAlmostEqual(ps[0], 0.0022159242059690038)
pmf = thinkstats2.Pmf(pdf)
self.assertAlmostEqual(pmf[1.0], 0.0239951295619)
xs, ps = pmf.Render()
self.assertEqual(xs[0], -5.0)
self.assertAlmostEqual(ps[0], 0.00026656181123)
cdf = thinkstats2.Cdf(pdf)
self.assertAlmostEqual(cdf[1.0], 0.51199756478094904)
xs, ps = cdf.Render()
self.assertEqual(xs[0], -5.0)
self.assertAlmostEqual(ps[0], 0.0)
def MakePdfExample(n=500):
"""Plots a normal density function and a KDE estimate.
n: sample size
"""
# mean and var of women's heights in cm, from the BRFSS
mean, var = 163, 52.8
std = math.sqrt(var)
# make a PDF and compute a density, FWIW
pdf = thinkstats2.NormalPdf(mean, std)
print(pdf.Density(mean + std))
# make a PMF and plot it
thinkplot.PrePlot(2)
thinkplot.Pdf(pdf, label='normal')
# make a sample, make an estimated PDF, and plot it
sample = [random.gauss(mean, std) for _ in range(n)]
sample_pdf = thinkstats2.EstimatedPdf(sample)
thinkplot.Pdf(sample_pdf, label='sample KDE')
thinkplot.Save(root='pdf_example', xlabel='Height (cm)', ylabel='Density')
#%% [markdown]
# ## 6.1 PDF
#
# - probability dencity function
#
# $PDF_{normal}(x) = \frac{1}{\sigma \sqrt{2\pi}}\exp[-\frac{1}{2}(\frac{x-\mu}{\sigma})^2]$
#%%
import thinkstats2
import math
mean, var = 163, 52.8
std = math.sqrt(var)
pdf = thinkstats2.NormalPdf(mean, std)
pdf.Density(mean + std)
#%%
import thinkplot
thinkplot.Pdf(pdf, label='normal')
thinkplot.Show(xlabel='height (cm)', ylabel='dencity')
#%%
pmf = pdf.MakePmf()
#%% [markdown]
# ## 6.2 KDE
#
# - Kernel density estimation
#%%
import random
sample = [random.gauss(mean, std) for _ in range(500)]