:py:mod:`ineqpy.grouped.stats`
==============================

.. py:module:: ineqpy.grouped.stats

.. autoapi-nested-parse::

   Stats' module.

   ..
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Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   ineqpy.grouped.stats.variance_hat_group
   ineqpy.grouped.stats.moment_group
   ineqpy.grouped.stats.quasivariance_hat_group



.. py:function:: variance_hat_group(data=None, variable='x', weights='w', group='h')

   
   Calculate variance.

   Data a DataFrame calculates the sample variance for each stratum. The
   objective of this function is to make it easy to calculate the moments of
   the distribution that follows an estimator, eg. Can be used to calculate
   the variance that follows the mean.

   :Parameters:

       **data** : pandas.DataFrame
           Dataframe containing the series needed for the calculation

       **x** : str
           ..

       **weights** : str
           Name of the weights `w` in the DataFrame

       **group** : str
           Name of the stratum variable `h` in the DataFrame

   :Returns:

       **vhat_h** : pandas.Series
           A series with the values of the variance of each `h` stratum.










   .. rubric:: Examples

   >>> # Computes the variance of the mean
   >>> data = pd.DataFrame(data=[renta, peso, estrato],
                           columns=["renta", "peso", "estrato"])
   >>> v = variance_hat_group(data)
   >>> v
   stratum
   1                700.917.728,64
   2              9.431.897.980,96
   3            317.865.839.789,10
   4            741.304.873.092,88
   5            535.275.436.859,10
   6            225.573.783.240,68
   7            142.048.272.010,63
   8             40.136.989.131,06
   9             18.501.808.022,56
   dtype: float64

   >>> # the value of de variance of the mean:
   >>> v_total = v.sum() / peso.sum() ** 2
       24662655225.947945



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.. py:function:: moment_group(data=None, variable='x', weights='w', group='h', order=2)

   
   Calculate the asymmetry of each `h` stratum.


   :Parameters:

       **variable** : array or str
           ..

       **weights** : array or str
           ..

       **group** : array or str
           ..

       **data** : pd.DataFrame, optional
           ..

       **order** : int, optional
           ..

   :Returns:

       **moment_of_order** : float
           ..













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.. py:function:: quasivariance_hat_group(data=None, variable=None, weights=None, group=None)

   
   Calculate quasivariance.

   Sample variance of `variable`, calculated as the second-order central
   moment.

   :Parameters:

       **data** : pd.DataFrame, optional
           pd.DataFrame that contains all variables needed.

       **variable** : array or str
           variable `x` apply the statistic. If `data` is None then must pass this
           argument as array, else as string name in `data`

       **weights** : array or str
           weights can be interpreted as frequency, probability,
           density function of `x`, each element in `x`. If `data` is None then
           must pass this argument as array, else as string name in `data`

       **group** : array or str
           group is a categorical variable to calculate the statistical by each
           group. If `data` is None then must pass this argument as array, else as
           string name in `data`

   :Returns:

       **shat2_group** : array or pd.Series
           ..








   .. rubric:: Notes

   This function is useful to calculate the variance of the mean.

   .. rubric:: References

   Moment (mathematics). (2017, May 6). In Wikipedia, The Free Encyclopedia.
   Retrieved 14:40, May 15, 2017, from
   https://en.wikipedia.org/w/index.php?title=Moment_(mathematics)&oldid=778996402

   .. only:: latex

      




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