chaospy.Normal

class chaospy.Normal(mu=0, sigma=1)

Normal (Gaussian) distribution

Args:

mu (float, Distribution):

Mean of the distribution.

sigma (float, Distribution):

Standard deviation. sigma > 0

Examples:

>>> distribution = chaospy.Normal(2, 3)
>>> distribution
Normal(mu=2, sigma=3)
>>> uloc = numpy.linspace(0, 1, 6)
>>> uloc
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>>> xloc = distribution.inv(uloc)
>>> xloc.round(3)
array([-22.66 ,  -0.525,   1.24 ,   2.76 ,   4.525,  26.66 ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0.   , 0.093, 0.129, 0.129, 0.093, 0.   ])
>>> distribution.sample(4).round(3)
array([ 3.185, -1.601,  6.943,  1.866])
>>> distribution.mom(1).round(3)
2.0
>>> distribution.ttr([0, 1, 2, 3]).round(3)
array([[ 2.,  2.,  2.,  2.],
       [ 0.,  9., 18., 27.]])

__init__(mu=0, sigma=1)

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.