jpt.distributions.univariate.gaussian
=====================================

.. py:module:: jpt.distributions.univariate.gaussian


Classes
-------

.. autoapisummary::

   jpt.distributions.univariate.gaussian.Gaussian


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

.. py:class:: Gaussian(mean=None, cov=None, data=None, weights=None)

   Bases: :py:obj:`dnutils.stats.Gaussian`


   Extension of :class:`dnutils.stats.Gaussian`

   Creates a new Gaussian distribution.

   :param mean:    the mean of the Gaussian
   :type mean:     float if multivariate else [float] if multivariate
   :param cov:     the covariance of the Gaussian
   :type cov:      float if multivariate else [[float]] if multivariate
   :param data:    if ``mean`` and ``cov`` are not provided, ``data`` may be a data set (matrix) from which the
                   parameters of the distribution are estimated.
   :type data:     [[float]]
   :param weights:  **[optional]** weights for the data points. The weight do not need to be normalized.
   :type weights:  [float]


   .. py:attribute:: PRECISION
      :value: 1e-15



   .. py:attribute:: _cl
      :value: 'jpt.distributions.univariate.gaussian.Gaussian'



   .. py:attribute:: _sum_w
      :value: 0



   .. py:attribute:: _sum_w_sq
      :value: 0



   .. py:attribute:: _mean


   .. py:attribute:: _cov


   .. py:attribute:: data
      :value: []



   .. py:method:: mean()


   .. py:method:: cov()


   .. py:method:: var()


   .. py:property:: std


   .. py:method:: deviation(x)

      Computes the deviation of ``x`` in multiples of the standard deviation.

      :param x:
      :type x:
      :returns:



   .. py:method:: __add__(alpha)


   .. py:method:: __radd__(other)


   .. py:method:: __iadd__(other)


   .. py:method:: __mul__(alpha)


   .. py:method:: __rmul__(other)


   .. py:method:: __imul__(other)


   .. py:method:: wasserstein_distance(d1: Gaussian, d2: Gaussian) -> float
      :staticmethod:



   .. py:method:: dim()


   .. py:method:: sample(n)

      Return ``n`` samples from this Gaussian distribution.

      :param n: number of samples
      :return: array of shape ``(n,)`` for 1-D or ``(n, d)`` for d-dimensional Gaussians



   .. py:property:: pdf


   .. py:method:: cdf(*x)


   .. py:method:: eval(lower, upper)


   .. py:method:: copy()


   .. py:method:: __eq__(other)


   .. py:method:: linreg()

      Compute a 4-tuple ``<m, b, rss, noise>`` of a linear regression represented by this Gaussian.

      :return:    ``m`` - the slope of the line
                  ``b`` - the intercept of the line
                  ``rss`` - the residual sum-of-squares error
                  ``noise`` - the square of the sample correlation coefficient ``r^2``

      References:
          - https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#In_least_squares_regression_analysis
          - https://milnepublishing.geneseo.edu/natural-resources-biometrics/chapter/chapter-7-correlation-and-simple-linear-regression/
          - https://en.wikipedia.org/wiki/Residual_sum_of_squares
          - https://en.wikipedia.org/wiki/Explained_sum_of_squares



   .. py:method:: update_all(data, weights=None)

      Update the distribution with new data points given in ``data``.



   .. py:method:: estimate(data, weights=None)

      Estimate the distribution parameters with subject to the given data points.



   .. py:method:: update(x, w=1)

      update the Gaussian distribution with a new data point ``x`` and weight ``w``.



   .. py:method:: retract(x, w=1)

      Retract the data point `x` with weight `w` from the Gaussian distribution.

      In case the data points are being kept in the distribution, it must actually exist and have the right
      weight associated. Otherwise, a ValueError will be raised.



   .. py:method:: sym()


   .. py:method:: plot(engine=None, **kwargs) -> Any

      Plots the distribution using the given engine.

      :param engine:  Can be either one of
          ``["plotly", "matplotlib"]``, or an instance of a
          rendering engine subclassing
          ``DistributionRendering``.
      :param kwargs:  The keyword arguments to pass to the
          engine as defined in the ``.plot_gaussian()``
          function of ``DistributionRendering`` or its
          respective subclass defined by ``engine``.
      :return:        the figure object of the plotting engine