chaospy.Nataf

class chaospy.Nataf(dist, covariance)

Nataf (normal) copula.

Examples:

>>> distribution = chaospy.Nataf(
...     chaospy.Iid(chaospy.Uniform(-1, 1), 2), covariance=[[1, .5], [.5, 1]])
>>> distribution
Nataf(Iid(Uniform(lower=-1, upper=1), 2), [[1.0, 0.5], [0.5, 1.0]])
>>> samples = distribution.sample(3)
>>> samples.round(4)
array([[ 0.3072, -0.77  ,  0.9006],
       [ 0.1262,  0.3001,  0.1053]])
>>> distribution.pdf(samples).round(4)
array([0.292 , 0.1627, 0.2117])
>>> distribution.fwd(samples).round(4)
array([[0.6536, 0.115 , 0.9503],
       [0.4822, 0.8725, 0.2123]])
>>> mesh = numpy.meshgrid([.4, .5, .6], [.4, .5, .6])
>>> distribution.inv(mesh).round(4)
array([[[-0.2   ,  0.    ,  0.2   ],
        [-0.2   ,  0.    ,  0.2   ],
        [-0.2   ,  0.    ,  0.2   ]],

       [[-0.2707, -0.1737, -0.0739],
        [-0.1008,  0.    ,  0.1008],
        [ 0.0739,  0.1737,  0.2707]]])

__init__(dist, covariance)

Args:

dist (Distribution):

The distribution to wrap.

covariance (numpy.ndarray):

Covariance matrix.

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.