.. _sphx_glr_api_gallery_statistics_likelihood:

Likelihood
----------

Maximum-likelihood fitting and the likelihood-ratio test.


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


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

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    <div class="sphx-glr-thumbcontainer" tooltip="Fits an exponential and a gamma distribution to the same skewed data by maximum likelihood, and plots the exponential model&#x27;s log-likelihood as a function of its scale: the curve peaks exactly at the sample mean, the closed-form MLE.">

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  .. image:: /api/gallery/statistics/likelihood/images/thumb/sphx_glr_plot_01_maximum_likelihood_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/likelihood/plot_01_maximum_likelihood`

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      <div class="sphx-glr-thumbnail-title">Fisher's maximum likelihood</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Repeatedly tests the true null hypothesis &quot;the normal mean is 0&quot; with the likelihood-ratio statistic 2(l1 - l0). Wilks&#x27;s theorem says the statistic&#x27;s null distribution approaches chi-square with one degree of freedom, the number of parameters the null hypothesis fixes.">

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  .. image:: /api/gallery/statistics/likelihood/images/thumb/sphx_glr_plot_02_wilks_likelihood_ratio_thumb.png
    :alt:

  :doc:`/api/gallery/statistics/likelihood/plot_02_wilks_likelihood_ratio`

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      <div class="sphx-glr-thumbnail-title">Wilks's theorem and the likelihood-ratio test</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/statistics/likelihood/plot_01_maximum_likelihood
   /api/gallery/statistics/likelihood/plot_02_wilks_likelihood_ratio