.. _sphx_glr_api_gallery_probability_branching:

Branching processes
--------------------

Galton-Watson extinction probabilities and simulated family trees.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Each man has 0, 1, or 2 sons with probabilities 0.2, 0.3, 0.5. The extinction probability is the smallest fixed point of the generating function G(s) = 0.2 + 0.3s + 0.5s^2, namely q = 0.4, even though the population grows by 30% per generation on average.">

.. only:: html

  .. image:: /api/gallery/probability/branching/images/thumb/sphx_glr_plot_01_galton_watson_thumb.png
    :alt:

  :doc:`/api/gallery/probability/branching/plot_01_galton_watson`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Galton-Watson: the probability a family name dies out</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/probability/branching/plot_01_galton_watson