pyuncertainnumber.pba.core
==========================

.. py:module:: pyuncertainnumber.pba.core


Classes
-------

.. autoapisummary::

   pyuncertainnumber.pba.core.Joint


Functions
---------

.. autoapisummary::

   pyuncertainnumber.pba.core.wasserstein_1d
   pyuncertainnumber.pba.core.area_metric_ecdf
   pyuncertainnumber.pba.core.endpoint_distance
   pyuncertainnumber.pba.core.area_metric_hint
   pyuncertainnumber.pba.core.distance_to_ecdf_bound
   pyuncertainnumber.pba.core.closer_bound
   pyuncertainnumber.pba.core.if_outside
   pyuncertainnumber.pba.core.if_right_in
   pyuncertainnumber.pba.core.directional
   pyuncertainnumber.pba.core.calibration_distance
   pyuncertainnumber.pba.core.slide_pbox_towards_scalar


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

.. py:class:: Joint(copula, marginals: list)

   Bases: :py:obj:`abc.ABC`


   Helper class that provides a standard way to create an ABC using
   inheritance.


   .. py:attribute:: copula


   .. py:attribute:: marginals


.. py:function:: wasserstein_1d(q1: numpy.typing.ArrayLike, q2: numpy.typing.ArrayLike, p: numpy.typing.ArrayLike) -> float

   An intuitive of Wasserstein metric in 1D, aka. area between two quantile functions

   This is equivaluent to the Area Metric in 1D, which shall return same results as "scipy.stats.wasserstein_distance"

   :param q1: quantile vectors (same length, corresponding to probabilities p)
   :type q1: ArrayLike
   :param q2: quantile vectors (same length, corresponding to probabilities p)
   :type q2: ArrayLike
   :param p: probability vector (between 0 and 1, monotone increasing)
   :type p: ArrayLike


.. py:function:: area_metric_ecdf(q1, q2, p)

   Wasserstein metric in 1D, aka. area between two quantile functions

   This is equivaluent to the Area Metric in 1D.

   :param q1: quantile vectors (same length, corresponding to probabilities p)
   :type q1: ArrayLike
   :param q2: quantile vectors (same length, corresponding to probabilities p)
   :type q2: ArrayLike
   :param p: probability vector (between 0 and 1, monotone increasing).
             Must be the same for q1 and q2
   :type p: ArrayLike


.. py:function:: endpoint_distance(A, B)

   Smallest endpoint distance elementwise between intervals.


.. py:function:: area_metric_hint()

.. py:function:: distance_to_ecdf_bound(x0, quantile)

   Min horizontal distance from x0 to the ECDF defined by quantile.


.. py:function:: closer_bound(x0, left_edge, right_edge)

   Decide which ECDF bound is closer to x0.

   :param x0: a scalar point
   :param left_edge: samples from the left bound of the ECDF
   :param x_right_samples: samples from the right bound of the ECDF


.. py:function:: if_outside(x0, left_edge, right_edge)

   Check if x0 is outside the ECDF defined by left_edge and right_edge.


.. py:function:: if_right_in(x0, left_edge, right_edge)

   Check if x0 is inside the ECDF defined by left_edge and right_edge.


.. py:function:: directional(x0, left_edge, right_edge)

   give instructions on which direction to move the Pbox towards the scalar

   :returns: output a message variable


.. py:function:: calibration_distance(a: pyuncertainnumber.pba.pbox_abc.Pbox, b: numbers.Number) -> float

   Estimate the calibration distance to compensate area metric between a P-box aand a scalar


.. py:function:: slide_pbox_towards_scalar(a, b)

   Slide the Pbox a towards the scalar b by one step.

   :param a: a Pbox
   :param b: a scalar

   :returns: a new Pbox that is slid towards b by one step