.. _book_fig_chapter4_fig_jackknife_gaussian:


Jackknife Calculations of Error on Mean
---------------------------------------
Figure 4.4.

The jackknife uncertainty estimates for the width of a Gaussian distribution.
This example uses the same data as figure 4.3. The upper panel shows a
histogram of the widths determined using the sample standard deviation, and
using the interquartile range. The lower panel shows the corrected jackknife
estimates (eqs. 4.33 and 4.35) for the two methods. The gray lines show the
theoretical results, given by eq. 3.35 for :math:`\sigma` and eq. 3.37 for
:math:`\sigma_G`. The result for :math:`\sigma` matches the theoretical
result almost exactly, but note the failure of the jackknife to correctly
estimate :math:`\sigma_G` (see the text for a discussion of this result).



.. image:: ../images/chapter4/fig_jackknife_gaussian_1.png
    :scale: 100
    :align: center


.. raw:: html
    
    <div class="toggle_trigger"><a href="#">

**Code output:**

.. raw:: html

    </a></div>
    <div class="toggle_container">

.. literalinclude:: fig_jackknife_gaussian.txt

.. raw:: html

    </div>
    <div class="toggle_trigger" id="start_open"><a href="#">

**Python source code:**

.. raw:: html

    </a></div>
    <div class="toggle_container">

.. literalinclude:: fig_jackknife_gaussian.py
    :lines: 16-

.. raw:: html

    </div>
    <div align="right">

:download:`[download source: fig_jackknife_gaussian.py] <fig_jackknife_gaussian.py>`

.. raw:: html
    
    </div>