== scipy.stats ==


{{{#!rst
The package `scipy.stats` provides tools for statistical analysis:

* More than 80 continuous distributions.
  A complete description of these distributions is available in LYX format in
  the source code directory. You can get a PDF version of this document here: `continuous.pdf <attachment:continuous.pdf>`_.

* More than 10 discrete distributions.
  A complete description of these distributions is available in LYX format in
  the source code directory. You can get a PDF version of this document here: `discrete.pdf <attachment:discrete.pdf>`_.

* Tools for manipulating them:

  + Statistical functions 
  + Statistical tests 
  + Statistical models 

}}}

== Kernel density estimation ==

stats.kde provides an object to do kernel density estimates (see http://www.maths.uwa.edu.au/~duongt/seminars/intro2kde/ ).

Here is an example using the gaussian kernel density estimator:
{{{
#!figure
#class right

inline:kde.png
}}}
{{{#!python
from pylab import plot, figure, imshow, xlabel, ylabel, cm, show
from scipy import stats, mgrid, c_, reshape, random, rot90

def measure(n):
    """ Measurement model, return two coupled measurements.
    """
    m1 = random.normal(size=n)
    m2 = random.normal(scale=0.5, size=n)
    return m1+m2, m1-m2

# Draw experiments and plot the results
m1, m2 = measure(2000)
xmin = m1.min()
xmax = m1.max()
ymin = m2.min()
ymax = m2.max()

# Perform a kernel density estimator on the results
X, Y = mgrid[xmin:xmax:100j, ymin:ymax:100j]
positions = c_[X.ravel(), Y.ravel()]
values = c_[m1, m2]
kernel = stats.kde.gaussian_kde(values.T)
Z = reshape(kernel(positions.T).T, X.T.shape)

figure(figsize=(3, 3))
imshow(     rot90(Z),
            cmap=cm.gist_earth_r,
            extent=[xmin, xmax, ymin, ymax])
plot(m1, m2, 'k.', markersize=2)

show()
}}}