.. _book_fig_chapter3_fig_clone_distribution:


Random Values from an Empirical Distribution
--------------------------------------------
Figure 3.25.

A demonstration of how to empirically clone a distribution, using a spline
interpolation to approximate the inverse of the observed cumulative
distribution. This allows us to nonparametrically select new random samples
approximating an observed distribution. First the list of points is sorted,
and the rank of each point is used to approximate the cumulative distribution
(upper right). Flipping the axes gives the inverse cumulative distribution on
a regular grid (lower left). After performing a cubic spline fit to the inverse
distribution, a uniformly sampled x value maps to a y value which approximates
the observed pdf. The lower-right panel shows the result. The K-S test
(see section 4.7.2) indicates that the samples are consistent with being
drawn from the same distribution. This method, while fast and effective,
cannot be easily extended to multiple dimensions.

This example uses the routine
:class:`astroML.density_estimation.EmpiricalDistribution`
to clone the distribution



.. image:: ../images/chapter3/fig_clone_distribution_1.png
    :scale: 100
    :align: center


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