Source code for copul.family.archimedean.nelsen15

import numpy as np
import sympy

from copul.family.archimedean.biv_archimedean_copula import BivArchimedeanCopula
from copul.family.frechet.lower_frechet import LowerFrechet




class GenestGhoudi(BivArchimedeanCopula):
    ac = BivArchimedeanCopula
    theta = sympy.symbols("theta", positive=True)
    theta_interval = sympy.Interval(1, np.inf, left_open=False, right_open=True)
    special_cases = {
        1: LowerFrechet,
    }
    _generator_at_0 = 1

    @property
    def is_absolutely_continuous(self) -> bool:
        return False

    @property
    def _raw_generator(self):
        return (1 - self.t ** (1 / self.theta)) ** self.theta

    @property
    def _raw_inv_generator(self):
        ind = sympy.Piecewise((1, self.y <= 1), (0, True))
        return (1 - self.y ** (1 / self.theta)) ** self.theta * ind

    @property
    def _cdf_expr(self):
        return (
            sympy.Max(
                1
                - (
                    (1 - self.u ** (1 / self.theta)) ** self.theta
                    + (1 - self.v ** (1 / self.theta)) ** self.theta
                )
                ** (1 / self.theta),
                0,
            )
            ** self.theta
        )



    def lambda_L(self):
        return 0




    def lambda_U(self):
        return 2 - 2 ** (1 / self.theta)




Nelsen15 = GenestGhoudi