chaospy.Gumbel

class chaospy.Gumbel(dist, theta)

Gumbel Copula.

\[\phi(x; \theta) = \frac{x^{-\theta}-1}{\theta} \phi^{-1}(q; \theta) = (q*\theta + 1)^{-1/\theta}\]

where \(\theta\) is defined on the interval [1,inf).

Examples:

>>> distribution = chaospy.Gumbel(
...     chaospy.Iid(chaospy.Uniform(-1, 1), 2), theta=2)
>>> distribution
Gumbel(Iid(Uniform(lower=-1, upper=1), 2), theta=2)
>>> samples = distribution.sample(3)
>>> samples.round(4)
array([[ 0.3072, -0.77  ,  0.9006],
       [ 0.4709,  0.2101,  0.8696]])
>>> distribution.pdf(samples).round(4)
array([7.9977000e+00, 5.0700000e-02, 3.6733563e+03])
>>> 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   ]],

       [[-0.0022,  0.1573,  0.3174],
        [ 0.109 ,  0.2591,  0.4062],
        [ 0.2181,  0.3564,  0.489 ]]])

__init__(dist, theta)

Args:

dist (Distribution):

The distribution to wrap

theta (float):

Copula parameter

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.