Source code for chaospy.distributions.collection.discrete_uniform

"""Discrete uniform probability distribution."""
import numpy
import chaospy

from ..baseclass import SimpleDistribution
from ..operators import J


class DiscreteUniform(SimpleDistribution):
    """
    Discrete uniform probability distribution.

    Examples:
        >>> distribution = chaospy.DiscreteUniform(2, 4)
        >>> distribution
        DiscreteUniform(2, 4)
        >>> qloc = numpy.linspace(0, 1, 9)
        >>> qloc.round(2)
        array([0.  , 0.12, 0.25, 0.38, 0.5 , 0.62, 0.75, 0.88, 1.  ])
        >>> distribution.inv(qloc).round(2)
        array([1.5 , 1.88, 2.25, 2.62, 3.  , 3.38, 3.75, 4.12, 4.5 ])
        >>> distribution.fwd(distribution.inv(qloc)).round(2)
        array([0.  , 0.12, 0.25, 0.38, 0.5 , 0.62, 0.75, 0.88, 1.  ])
        >>> distribution.pdf(distribution.inv(qloc)).round(4)
        array([0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5])
        >>> distribution.sample(4)
        array([3, 2, 4, 3])
        >>> distribution.mom(1).round(4)
        3.0

    """

    interpret_as_integer = True

    def __init__(self, lower, upper):
        """
        Args:
            lower (float, chaospy.Distribution):
                Lower threshold of distribution. Must be smaller than
                ``upper``. Value will be rounded up to closes integer.
            upper (float, chaospy.Distribution):
                Upper threshold of distribution. Value will be rounded down to
                closes integer.
        """
        super(DiscreteUniform, self).__init__(dict(lower=lower, upper=upper))
        self._repr_args = [lower, upper]

    def _cdf(self, x_data, lower, upper):
        """Cumulative distribution function."""
        lower = numpy.round(lower)
        upper = numpy.round(upper)
        out = (x_data - lower + 0.5) / (upper - lower + 1)
        return out

    def _lower(self, lower, upper):
        """Lower bounds."""
        return numpy.round(lower) - 0.5 + 1e-10

    def _upper(self, lower, upper):
        """Upper bounds."""
        return numpy.round(upper) + 0.5 - 1e-10

    def _pdf(self, x_data, lower, upper):
        """Probability density function."""
        return x_data**0 / (numpy.round(upper) - numpy.round(lower))

    def _ppf(self, q_data, lower, upper):
        """Point percentile function."""
        lower = numpy.round(lower)
        upper = numpy.rint(upper)
        return q_data * (upper - lower + 1) + lower - 0.5

    def _mom(self, k_data, lower, upper):
        """Raw statistical moments."""
        return numpy.mean(
            numpy.arange(numpy.ceil(lower), numpy.floor(upper) + 1) ** k_data
        )