arbitragelab.copula_approach.mixed_copulas.base

Class template for mixed copulas.

Module Contents

Classes

MixedCopula

Class template for mixed copulas.
class MixedCopula(copula_name: str)

Bases: arbitragelab.copula_approach.base.Copula, abc.ABC

Class template for mixed copulas.

__slots__ = ()
describe() → pandas.Series

Describe the components and coefficients of the mixed copula.

The description includes descriptive name, class name, the copula dependency parameter for each mixed copula component and their weights.

Returns:

(pd.Series) The description of the specific mixed copula.

get_cop_density(u: float, v: float, eps: float = 1e-05) → float

Calculate probability density of the bivariate copula: P(U=u, V=v).

Result is analytical. Also the u and v will be remapped into [eps, 1-eps] to avoid edge values that may result in infinity or NaN.

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

  • eps – (float) Optional. The distance to the boundary 0 or 1, such that the value u, v will be mapped back. Defaults to 1e-5.

Returns:

(float) The probability density (aka copula density).

get_cop_eval(u: float, v: float, eps: float = 0.0001) → float

Calculate cumulative density of the bivariate copula: P(U<=u, V<=v).

Result is analytical except for Student-t copula. Also at the u and v will be remapped into [eps, 1-eps] to avoid edge values that may result in infinity or NaN.

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

  • eps – (float) Optional. The distance to the boundary 0 or 1, such that the value u, v will be mapped back. Defaults to 1e-4.

Returns:

(float) The cumulative density.

get_condi_prob(u: float, v: float, eps: float = 1e-05) → float

Calculate conditional probability function: P(U<=u | V=v).

Result is analytical. Also at the u and v will be remapped into [eps, 1-eps] to avoid edge values that may result in infinity or NaN.

Note: This probability is symmetric about (u, v).

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

  • eps – (float) Optional. The distance to the boundary 0 or 1, such that the value u, v will be mapped back. Defaults to 1e-5.

Returns:

(float) The conditional probability.

sample(num: int) → numpy.array

Generate pairs according to P.D.F., stored in a 2D np.array of shape (num, 2).

Parameters:

num – (int) Number of points to generate.

Return sample_pairs:

(np.array) Shape=(num, 2) array, sampled data for this copula.

static theta_hat(tau: float) → float

Calculate theta hat from Kendall’s tau from sample data.

Parameters:

tau – (float) Kendall’s tau from sample data.

Returns:

(float) The associated theta hat for this very copula.

get_log_likelihood_sum(u: numpy.array, v: numpy.array) → float

Get log-likelihood value sum.

Parameters:

  • u – (np.array) 1D vector data of X pseudo-observations. Need to be uniformly distributed [0, 1].

  • v – (np.array) 1D vector data of Y pseudo-observations. Need to be uniformly distributed [0, 1].

Returns:

(float) Log-likelihood sum value.

c(u: float, v: float) → float

Placeholder for calculating copula density.

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

C(u: float, v: float) → float

Placeholder for calculating copula evaluation.

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

condi_cdf(u: float, v: float) → float

Placeholder for calculating copula conditional probability.

Parameters:

  • u – (float) A real number in [0, 1].

  • v – (float) A real number in [0, 1].

fit(u: numpy.array, v: numpy.array) → float

Fit copula to empirical data (pseudo-observations). Once fit, self.theta is updated.

Parameters:

  • u – (np.array) 1D vector data of X pseudo-observations. Need to be uniformly distributed [0, 1].

  • v – (np.array) 1D vector data of Y pseudo-observations. Need to be uniformly distributed [0, 1].

Returns:

(float) Theta hat estimate for fit copula.

plot_cdf(plot_type: str = '3d', grid_size: int = 50, levels: list = None, **kwargs) → matplotlib.pyplot.axis

Plot either ‘3d’ or ‘contour’ plot of copula CDF.

Parameters:

  • plot_type – (str) Either ‘3d’ or ‘contour’(2D) plot.

  • grid_size – (int) Mesh grid granularity.

  • kwargs – (dict) User-specified params for ‘ax.plot_surface’/’plt.contour’.

  • levels – (list) List of float values that determine the number and levels of lines in a contour plot. If not provided, these are calculated automatically.

Returns:

(plt.axis) Axis object.

plot_scatter(num_points: int = 100) → matplotlib.axes.Axes

Plot copula scatter plot of generated pseudo-observations.

Parameters:

num_points – (int) Number of samples to generate.

Returns:

(plt.axis) Axis object.

plot_pdf(plot_type: str = '3d', grid_size: int = 50, levels: list = None, **kwargs) → matplotlib.figure.Figure

Plot either ‘3d’ or ‘contour’ plot of copula PDF.

Parameters:

  • plot_type – (str) Either ‘3d’ or ‘contour’(2D) plot.

  • grid_size – (int) Mesh grid granularity.

  • levels – (list) List of float values that determine the number and levels of lines in a contour plot. If not provided, these are calculated automatically.

Returns:

(plt.axis) Axis object.