iact_estimator.statistics
=========================

.. py:module:: iact_estimator.statistics

.. autoapi-nested-parse::

   Functions that implement some statistical formulas.

   ..
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Functions
---------

.. autoapisummary::

   iact_estimator.statistics.sigma_to_probability
   iact_estimator.statistics.probability_to_sigma
   iact_estimator.statistics.significance_li_ma


Module Contents
---------------

.. py:function:: sigma_to_probability(sigma)

   
   Convert significance to one side of the two-sided probability.


   :Parameters:

       **sigma** : float
           Significance value.



   :Returns:

       **probability** : float
           Probability value.











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.. py:function:: probability_to_sigma(probability)

   
   Inversion function of `.sigma_to_probability()`.


   :Parameters:

       **probability** : float
           Probability value.



   :Returns:

       **sigma** : float
           Significance value.











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.. py:function:: significance_li_ma(n_on, n_off, alpha, mu_sig=None)

   
   Get the Li & Ma significance.

   This is equivalent to eq.17 of [R5376e64402a7-1]_.

   :Parameters:

       **n_on** : `int`
           Measured counts in ON region.

       **n_off** : `int`
           Measured counts in OFF region.

       **alpha** : `float`
           Acceptance ratio of ON and OFF measurements.

       **mu_sig** : `float`
           Expected signal counts in ON region.



   :Returns:

       **sqrt_ts** : `float``
           Significance as the square root of the Test Statistic.








   .. rubric:: Notes

   The implementation uses `gammapy.stats.WStatCountsStatistic`
   and takes the square root of the Test Statistic.

   .. rubric:: References

   .. [R5376e64402a7-1] Li, T.-P. & Ma, Y.-Q., ApJ, 1983, 272, 317, 10.1086/161295.

   .. only:: latex

      [R5376e64402a7-1]_


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