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Kernel Density Estimation

In [1]:
%matplotlib inline

import numpy as np
from scipy import stats
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.distributions.mixture_rvs import mixture_rvs

A univariate example.

In [2]:
np.random.seed(12345)
In [3]:
obs_dist1 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.norm],
                kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
In [4]:
kde = sm.nonparametric.KDEUnivariate(obs_dist1)
kde.fit()
In [5]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.hist(obs_dist1, bins=50, normed=True, color='red')
ax.plot(kde.support, kde.density, lw=2, color='black');
In [6]:
obs_dist2 = mixture_rvs([.25,.75], size=10000, dist=[stats.norm, stats.beta],
            kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=1,args=(1,.5))))

kde2 = sm.nonparametric.KDEUnivariate(obs_dist2)
kde2.fit()
In [7]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.hist(obs_dist2, bins=50, normed=True, color='red')
ax.plot(kde2.support, kde2.density, lw=2, color='black');

The fitted KDE object is a full non-parametric distribution.

In [8]:
obs_dist3 = mixture_rvs([.25,.75], size=1000, dist=[stats.norm, stats.norm],
                kwargs = (dict(loc=-1,scale=.5),dict(loc=1,scale=.5)))
kde3 = sm.nonparametric.KDEUnivariate(obs_dist3)
kde3.fit()
In [9]:
kde3.entropy
Out[9]:
1.3343301918419768
In [10]:
kde3.evaluate(-1)
Out[10]:
array([ 0.17992591])

CDF

In [11]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.plot(kde3.support, kde3.cdf);

Cumulative Hazard Function

In [12]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.plot(kde3.support, kde3.cumhazard);

Inverse CDF

In [13]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.plot(kde3.support, kde3.icdf);

Survival Function

In [14]:
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
ax.plot(kde3.support, kde3.sf);

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.
http://www.statsmodels.org/stable/examples/notebooks/generated/kernel_density.html