python source code of binomial

Project: chaospy (GitHub Link)

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        chebyshev.py
        primes.py
        korobov.py
        grid.py
        hammersley.py
        __init__.py
        halton.py
        sobol.py
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- conftest.py

"""Binomial probability distribution."""
from functools import wraps
import numpy
from scipy import special

from ..baseclass import Dist


class Binomial(Dist):
    """
    Binomial probability distribution.

    Point density:
        comb(N, x) p^x (1-p)^{N-x}      x in {0, 1, ..., N}

    Examples:
        >>> distribution = chaospy.Binomial(5, 0.5)
        >>> distribution
        Binomial(prob=0.5, size=5)
        >>> q = numpy.linspace(0, 1, 8)
        >>> distribution.inv(q)
        array([0, 1, 2, 2, 3, 3, 4, 5])
        >>> distribution.fwd(distribution.inv(q)).round(4)
        array([0.0312, 0.1875, 0.5   , 0.5   , 0.8125, 0.8125, 0.9688, 1.    ])
        >>> distribution.pdf(distribution.inv(q)).round(4)
        array([0.0312, 0.1562, 0.3125, 0.3125, 0.3125, 0.3125, 0.1562, 0.0312])
        >>> distribution.sample(10)
        array([3, 1, 4, 2, 4, 2, 1, 2, 2, 4])
        >>> distribution.mom([1, 2, 3]).round(4)
        array([ 2.5,  7.5, 25. ])
        >>> distribution.ttr([1, 2, 3]).round(4)
        array([[2.5 , 2.5 , 2.5 ],
               [1.25, 2.  , 2.25]])
    """
    interpret_as_integer = True

    def __init__(self, size, prob):
        self._repr = {"size": size, "prob": prob}
        Dist.__init__(self, size=size, prob=prob)

    def _cdf(self, x_data, size, prob):
        return special.bdtr(numpy.floor(x_data), numpy.floor(size), prob)

    def _ppf(self, q_data, size, prob):
        return numpy.ceil(special.bdtrik(q_data, numpy.floor(size), prob))

    def _pdf(self, x_data, size, prob):
        return special.comb(size, x_data)*prob**x_data*(1-prob)**(size-x_data)

    def _lower(self, size, prob):
        return 0

    def _upper(self, size, prob):
        return numpy.floor(size)+1

    def _mom(self, k_data, size, prob):
        x_data = numpy.arange(int(size)+1, dtype=int)
        return numpy.sum(x_data**k_data*self._pdf(
            x_data, size=numpy.floor(size), prob=prob))

    def _ttr(self, k_data, size, prob):
        """Krawtchouk rule"""
        from chaospy.quadrature import discretized_stieltjes
        abscissas = numpy.arange(0, numpy.floor(size)+1)
        weights = self._pdf(abscissas, size, prob)
        (alpha, beta), _, _ = discretized_stieltjes(k_data, [abscissas], weights)
        return alpha[0, -1], beta[0, -1]