.. _stats:

***************************************
Astrostatistics Tools (`astropy.stats`)
***************************************

Introduction
============

The `astropy.stats` package holds statistical functions or algorithms
used in astronomy.  While the `scipy.stats` and `statsmodel
<http://www.statsmodels.org/stable/index.html>`_ packages contains a
wide range of statistical tools, they are general-purpose packages and
are missing some tools that are particularly useful or specific to
astronomy.  This package is intended to provide such functionality,
but *not* to replace `scipy.stats` if its implementation satisfies
astronomers' needs.


Getting Started
===============

A number of different tools are contained in the stats package, and
they can be accessed by importing them::

    >>> from astropy import stats

A full list of the different tools are provided below.  Please see the
documentation for their different usage.  For example, sigma clipping,
which is common way to estimate the background of an image, can be
performed with the :func:`~astropy.stats.sigma_clip` function.  By
default, the function returns a masked array where outliers are
masked::

    >>> data = [1, 5, 6, 8, 100, 5, 3, 2]
    >>> stats.sigma_clip(data, sigma=2, maxiters=5)  # doctest: +SKIP
    masked_array(data=[1, 5, 6, 8, --, 5, 3, 2],
                 mask=[False, False, False, False,  True, False, False, False],
           fill_value=999999)

.. above and below, skipped masked_array tests can be included when we know
   "not NUMPY_LT_1_14"

Alternatively, the :class:`~astropy.stats.SigmaClip` class provides an
object-oriented interface to sigma clipping, which also returns a
masked array by default::

    >>> sigclip = stats.SigmaClip(sigma=2, maxiters=5)
    >>> sigclip(data)  # doctest: +SKIP
    masked_array(data=[1, 5, 6, 8, --, 5, 3, 2],
                 mask=[False, False, False, False,  True, False, False, False],
           fill_value=999999)

In addition, there are also several convenience functions for making
the calculation of statistics even easier.  For example,
:func:`~astropy.stats.sigma_clipped_stats` will return the mean,
median, and standard deviation of a sigma-clipped array::

     >>> stats.sigma_clipped_stats(data, sigma=2, maxiters=5)  # doctest: +FLOAT_CMP
     (4.2857142857142856, 5.0, 2.2497165354319457)

There are also tools for calculating :ref:`robust statistics
<stats-robust>`, sampling the data, :ref:`circular statistics
<stats-circular>`, confidence limits, spatial statistics, and adaptive
histograms.

Most tools are fairly self-contained, and include relevant examples in
their docstrings.


Using `astropy.stats`
=====================

More detailed information on using the package is provided on separate pages,
listed below.

.. toctree::
   :maxdepth: 2

   robust.rst
   circ.rst
   lombscargle.rst
   bls.rst
   ripley.rst
   ../visualization/histogram.rst


Constants
=========

The `astropy.stats` package defines two constants useful for
converting between Gaussian sigma and full width at half maximum
(FWHM):

.. data:: gaussian_sigma_to_fwhm

    Factor with which to multiply Gaussian 1-sigma standard deviation
    to convert it to full width at half maximum (FWHM).

    >>> from astropy.stats import gaussian_sigma_to_fwhm
    >>> gaussian_sigma_to_fwhm  # doctest: +FLOAT_CMP
    2.3548200450309493

.. data:: gaussian_fwhm_to_sigma

    Factor with which to multiply Gaussian full width at half maximum
    (FWHM) to convert it to 1-sigma standard deviation.

    >>> from astropy.stats import gaussian_fwhm_to_sigma
    >>> gaussian_fwhm_to_sigma  # doctest: +FLOAT_CMP
    0.42466090014400953


See Also
========

* :mod:`scipy.stats`
    This scipy package contains a variety of useful statistical functions and
    classes.  The functionality in `astropy.stats` is intended to supplement
    this, *not* replace it.

* `statsmodel <http://www.statsmodels.org/stable/index.html>`_
    The statsmodel package provides functionality for estimating
    different statistical models, tests, and data exploration.

* `astroML <http://www.astroml.org/>`_
    The astroML package is a Python module for machine learning and
    data mining.  Some of the tools from this package have been
    migrated here, but there are still a number of tools there that
    are useful for astronomy and statistical analysis.


* :func:`astropy.visualization.hist`
    The :func:`~astropy.stats.histogram` routine and related functionality
    defined here are used within the :func:`astropy.visualization.hist`
    function. For a discussion of these methods for determining histogram
    binnings, see :ref:`astropy-visualization-hist`.

.. note that if this section gets too long, it should be moved to a separate 
   doc page - see the top of performance.inc.rst for the instructions on how to do 
   that
.. include:: performance.inc.rst

Reference/API
=============

.. automodapi:: astropy.stats