Bivariate Copula base class. More...

Inheritance diagram for starvine.bvcopula.copula.copula_base.CopulaBase:

Public Member Functions
def	__init__ (self, rotation=0)
	Init copula. More...

def	cdf (self, u, v, theta)
	Evaluate the copula's CDF function. More...

def	pdf (self, u, v, theta)
	Public facing PDF function. More...

def	h (self, u, v, theta)

def	hinv (self, u, v, theta)

def	fitMLE (self, u, v, theta0, kwargs)
	Maximum likelyhood copula fit. More...

def	sample (self, n=1000, mytheta)
	Draw N samples from the copula. More...

def	setRotation (self, rotation=0)
	Set the copula's orientation: Allows for modeling negative dependence with the frank, gumbel, and clayton copulas (Archimedean Copula family is non-symmetric) More...

def	kTau (self, rotation=0, theta)
	Public facing kendall's tau function.

Public Attributes
	rotation

	fittedParams

Private Member Functions
def	_pdf (self, u, v, rotation=0, theta)
	Pure virtual density function. More...

def	_cdf (self, u, v, rotation=0, theta)
	Default implementation of the cumulative density function. More...

def	_ppf (self, u, v, rotation=0, theta)
	Percentile point function. More...

def	_h (self, u, v, rotation=0, theta)
	Copula conditional distribution function. More...

def	_hinv (self, u, v, rotation=0, theta)
	Inverse H function.

def	_v (self, u, v, rotation=0, theta)
	Copula conditional distribution function. More...

def	_vinv (self, u, v, rotation=0, theta)

def	_nlogLike (self, u, v, rotation=0, theta)
	Default negative log likelyhood function. More...

def	_logLike (self, u, v, rotation=0, theta)
	Default log likelyhood func.

def	_invhfun_bisect (self, U, V, rotation, theta)
	Compute inverse of H function using bisection. More...

def	_AIC (self, u, v, rotation=0, theta)
	Estimate the AIC of a fitted copula (with params == theta) More...

def	_gen (self, t, theta)
	Copula generator function.

def	_kTau (self, rotation=0, theta)
	Computes Kendall's tau. More...

def	_rotPDF (cls, f)
	Define copula probability density function rotation.

def	_rotCDF (cls, f)
	Define copula cumulative density function rotation.

def	_rotHinv (cls, f)
	Define copula dependence function rotation.

def	_rotH (cls, f)
	Define copula inverse dependence function rotation.

def	_rotGen (cls, f)
	Copula generator wrapper.

Detailed Description

Bivariate Copula base class.

Meant to be subclassed with the PDF and CDF methods being overridden for a given specific copula.

Copula can be rotated by 90, 180, 270 degrees to accommodate negative dependence.

Constructor & Destructor Documentation

§ init()

def starvine.bvcopula.copula.copula_base.CopulaBase.__init__	(	self,
		rotation = `0`
	)

Init copula.

Parameters

rotation int Copula orientation

Member Function Documentation

§ _AIC()

def starvine.bvcopula.copula.copula_base.CopulaBase._AIC	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Estimate the AIC of a fitted copula (with params == theta)

Parameters

theta Copula paramter list

§ _cdf()

def starvine.bvcopula.copula.copula_base.CopulaBase._cdf	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Default implementation of the cumulative density function.

Very slow. Recommended to replace with an analytic CDF if possible.

Parameters

theta	Copula parameter list
rotation	int copula rotation parameter
u	np_1darray Rank CDF data vector
v	np_1darray Rank CDF data vector

§ _h()

def starvine.bvcopula.copula.copula_base.CopulaBase._h	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Copula conditional distribution function.

Provides $ h $ given $ V $ and $\theta$ .

$h(u|v, \theta) = \frac{\partial C( F(u|v), F(u|v) | \theta) }{\partial F(u|v)}$

Parameters

u	np_1darray is uniformly distributed on [0, 1]
v	np_1darray is distributed acording to some some known DF
rotation	Copula rotation paramter
theta	Known copula paramter list

Returns: h $h(u|v, \theta)$

§ _invhfun_bisect()

def starvine.bvcopula.copula.copula_base.CopulaBase._invhfun_bisect	(	self,
		U,
		V,
		rotation,
		theta
	)

private

Compute inverse of H function using bisection.

Update (11/08/2016) performance improvement: finish with newton iterations Update (12/04/2016) Newton can minimization needs bounds checks! TODO: move to scipy.minmize

§ _kTau()

def starvine.bvcopula.copula.copula_base.CopulaBase._kTau	(	self,
		rotation = `0`,
		theta
	)

private

Computes Kendall's tau.

Requires that the copula has a _gen() method implemented. This method should be overridden if an analytic form of kendall's tau is avalible.

Let $ T = C(u, v) $ represent a random variable and $ t $ is an RV distributed according to $ T() $ .

$K_c(t) = \frac{\phi(t)}{\phi'(t)}$

$\tau = 1 + 4 \int_0^1 K_c(t) dt$

where $\phi(t)$ is the copula generating function.

Note: For the gauss and students-t copula:

$\tau = \frac{2.0}{\pi} arcsin(\rho)$

where $\rho$ is the linear correlation coefficient.

§ _nlogLike()

def starvine.bvcopula.copula.copula_base.CopulaBase._nlogLike	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Default negative log likelyhood function.

Used in MLE fitting

§ _pdf()

def starvine.bvcopula.copula.copula_base.CopulaBase._pdf	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Pure virtual density function.

Parameters

u	np_1darray Rank CDF data vector
v	np_1darray Rank CDF data vector
rotation_theta	int Copula rotation (0 == 0deg, 1==90deg, ...)

§ _ppf()

def starvine.bvcopula.copula.copula_base.CopulaBase._ppf	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Percentile point function.

Equivilent to the inverse of the CDF. Used to draw random samples from the bivariate distribution.

EX: will draw 100 samples from a t-copula with params [0.21, 20]

>>> import starvine.bvcopula as bvc
>>> My_Copula = bvc.t_copula.StudentTCopula()
>>> u, v = np.random.uniform(0, 1, 100)
>>> My_Copula._ppf(u, v, rotation=0, 0.21, 20)

§ _v()

def starvine.bvcopula.copula.copula_base.CopulaBase._v	(	self,
		u,
		v,
		rotation = `0`,
		theta
	)

private

Copula conditional distribution function.

Provides $ V$ given $ u $ and $\theta$

§ cdf()

def starvine.bvcopula.copula.copula_base.CopulaBase.cdf	(	self,
		u,
		v,
		theta
	)

Evaluate the copula's CDF function.

Parameters

u	np_1darray Rank data vector
v	np_1darray Rank data vector
theta	list of float Copula parameter list

§ fitMLE()

def starvine.bvcopula.copula.copula_base.CopulaBase.fitMLE	(	self,
		u,
		v,
		theta0,
		kwargs
	)

Maximum likelyhood copula fit.

Parameters

u	np_1darray Rank data vector
v	np_1darray Rank data vector
theta0	Initial guess for copula parameter list

Returns: tuple : (np_array Array of MLE fit copula parameters, int Fitting success flag, 1==success)

§ pdf()

def starvine.bvcopula.copula.copula_base.CopulaBase.pdf	(	self,
		u,
		v,
		theta
	)

Public facing PDF function.

Parameters

u	np_1darray Rank data vector
v	np_1darray Rank data vector
theta	list of float Copula parameter list

§ sample()

def starvine.bvcopula.copula.copula_base.CopulaBase.sample	(	self,
		n = `1000`,
		mytheta
	)

Draw N samples from the copula.

Parameters

n	Number of samples
theta	Parameter list
rotation	Copula rotation parameter

Returns: np_array (n, 2) size vector. Resampled (U, V) data pairs from copula with paramters: *theta

§ setRotation()

def starvine.bvcopula.copula.copula_base.CopulaBase.setRotation	(	self,
		rotation = `0`
	)

Set the copula's orientation: Allows for modeling negative dependence with the frank, gumbel, and clayton copulas (Archimedean Copula family is non-symmetric)

Parameters

rotation int Copula rotation. 0 == 0 deg, 1 == 90 deg rotation, 2 == 180 deg rotation, 3 == 270 deg rotation

The documentation for this class was generated from the following file:

starvine/bvcopula/copula/copula_base.py

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

§ __init__()

Member Function Documentation

§ _AIC()

§ _cdf()

§ _h()

§ _invhfun_bisect()

§ _kTau()

§ _nlogLike()

§ _pdf()

§ _ppf()

§ _v()

§ cdf()

§ fitMLE()

§ pdf()

§ sample()

§ setRotation()

§ init()