.. npdist.rst

.. py:currentmodule:: dit

Joint Distributions
===================

The primary method of constructing a distribution is by supplying both the
outcomes and the probability mass function:

.. ipython::

   In [1]: from dit import Distribution

   In [2]: outcomes = ['000', '011', '101', '110']

   In [3]: pmf = [1/4]*4

   In [4]: xor = Distribution(outcomes, pmf)

   @doctest
   In [5]: print(xor)
   Class:          Distribution
   Alphabet:       ('0', '1') for all rvs
   Base:           linear
   Outcome Class:  str
   Outcome Length: 3
   RV Names:       None
   x     p(x)
   000   0.25
   011   0.25
   101   0.25
   110   0.25

Another way to construct a distribution is by supplying a dictionary mapping
outcomes to probabilities:

.. ipython::

   In [6]: outcomes_probs = {'000': 1/4, '011': 1/4, '101': 1/4, '110': 1/4}

   In [7]: xor2 = Distribution(outcomes_probs)

   @doctest
   In [8]: print(xor2)
   Class:          Distribution
   Alphabet:       ('0', '1') for all rvs
   Base:           linear
   Outcome Class:  str
   Outcome Length: 3
   RV Names:       None
   x     p(x)
   000   0.25
   011   0.25
   101   0.25
   110   0.25

Yet a third method is via an ndarray:

.. ipython::

    In [9]: pmf = [[0.5, 0.25], [0.25, 0]]

    In [10]: d = Distribution.from_ndarray(pmf)

    @doctest
    In [11]: print(d)
    Class:          Distribution
    Alphabet:       (0, 1) for all rvs
    Base:           linear
    Outcome Class:  tuple
    Outcome Length: 2
    RV Names:       None
    x       p(x)
    (0, 0)  0.5
    (0, 1)  0.25
    (1, 0)  0.25

.. automethod:: Distribution.__init__

To verify that these two distributions are the same, we can use the
`is_approx_equal` method:

.. ipython::

   @doctest
   In [12]: xor.is_approx_equal(xor2)
   Out[12]: True

.. automethod:: Distribution.is_approx_equal