chaospy.StudentT

class chaospy.StudentT(df=1, mu=0, sigma=1)

(Non-central) Student-t distribution.

Args:

df (float, Distribution):

Degrees of freedom.

loc (float, Distribution):

Location parameter.

scale (float, Distribution):

Scale parameter.

Examples:

>>> distribution = chaospy.StudentT(10)
>>> distribution
StudentT(10)
>>> 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([-102.051,   -0.879,   -0.26 ,    0.26 ,    0.879,  100.988])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0.   , 0.258, 0.375, 0.375, 0.258, 0.   ])
>>> distribution.sample(4).round(3)
array([ 0.407, -1.278,  1.816, -0.046])
>>> distribution.mom(1).round(3)
0.0
>>> distribution.ttr([0, 1, 2, 3]).round(3)
array([[ 0.  ,  0.  ,  0.  ,  0.  ],
       [ 0.  ,  1.25,  3.75, 10.  ]])

__init__(df=1, 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.