chaospy.Binomial

class chaospy.Binomial(size, prob)

Binomial probability distribution.

Point density:

comb(N, x) p^x (1-p)^{N-x} x in {0, 1, …, N}

Examples:

>>> distribution = chaospy.Binomial(3, 0.5)
>>> distribution
Binomial(3, 0.5)
>>> xloc = numpy.arange(4)
>>> distribution.pdf(xloc).round(4)
array([0.125, 0.375, 0.375, 0.125])
>>> distribution.cdf(xloc).round(4)
array([0.125, 0.5  , 0.875, 1.   ])
>>> distribution.fwd([-0.5, -0.49, 0, 0.49, 0.5]).round(4)
array([0.    , 0.0013, 0.0625, 0.1238, 0.125 ])
>>> uloc = numpy.linspace(0, 1, 8)
>>> uloc.round(2)
array([0.  , 0.14, 0.29, 0.43, 0.57, 0.71, 0.86, 1.  ])
>>> distribution.inv(uloc).round(2)
array([-0.5 ,  0.55,  0.93,  1.31,  1.69,  2.07,  2.45,  3.5 ])
>>> distribution.sample(10)
array([1, 3, 2, 1, 0, 1, 1, 0, 2, 1])
>>> distribution.mom([1, 2, 3]).round(4)
array([1.5 , 3.  , 6.75])

__init__(size, prob)

Distribution initializer.

In addition to assigning some object variables, also checks for some consistency issues.

Args:

parameters (Optional[Distribution[str, Union[ndarray, Distribution]]]):

Collection of model parameters.

dependencies (Optional[Sequence[Set[int]]]):

Dependency identifiers. One collection for each dimension.

rotation (Optional[Sequence[int]]):

The order of which to resolve dependencies.

exclusion (Optional[Sequence[int]]):

Distributions that has been “taken out of play” and therefore can not be reused other places in the dependency hierarchy.

repr_args (Optional[Sequence[str]]):

Positional arguments to place in the object string representation. The repr output will then be: <class name>(<arg1>, <arg2>, …).

Raises:

StochasticallyDependentError:

For dependency structures that can not later be rectified. This include under-defined distributions, and inclusion of distributions that should be exclusion.

Methods

pdf(x_data[, decompose, allow_approx, step_size])	Probability density function.
cdf(x_data)	Cumulative distribution function.
fwd(x_data)	Forward Rosenblatt transformation.
inv(q_data[, max_iterations, tollerance])	Inverse Rosenblatt transformation.
sample([size, rule, antithetic, ...])	Create pseudo-random generated samples.
mom(K[, allow_approx])	Raw statistical moments.
ttr(kloc)	Three terms relation's coefficient generator.

Attributes

interpret_as_integer	Flag indicating that return value from the methods sample, and inv should be interpreted as integers instead of floating point.
lower	Lower bound for the distribution.
stochastic_dependent	True if distribution contains stochastically dependent components.
upper	Upper bound for the distribution.