igcop: Computational Tools for the IG and IGL Copula Families

Description

Compute distributional quantities for an Integrated Gamma (IG) or IG Limit (IGL) copula, such as a cdf and density, along with conditional quantities such as the cdf, quantiles, and densities. Generate data from a copula.

Usage

Access copula quantities by starting with the p, d, q, or r prefixes, followed by the copula name – either ig or igl, or their conditional versions, condig or condigl.

Author(s)

Maintainer: Vincenzo Coia vincenzo.coia@gmail.com

Authors:

• Harry Joe

Clean up DLL

Description

As recommended in the "Compiled Code" chapter of the book "R packages" (Version 2) by Hadley Wickham and Jenny Bryan.

Usage

.onUnload(libpath)

Arguments

Test data

Description

Internal data used in the test scripts. .u and .v are vectors of matching length containing values between 0 and 1 and reasonably cover the unit square. .cpar is a list of IG copula parameter pairs c(theta, alpha), and .theta and .alpha are the corresponding (unique) individual values.

Usage

.u

.v

.cpar

.theta

.alpha

Format

Everything is a numeric vector, except .cpar, which is a list of bivariate numeric vectors. .u and .v are of matching length; the rest are not intended to have matching lengths.

An object of class numeric of length 17.

An object of class list of length 25.

An object of class numeric of length 14.

An object of class numeric of length 11.

Check validity of copula parameters

Description

Ensures input values are non-negative.

Usage

check_alpha(alpha)

check_theta(theta)

Arguments

Value

An error if any theta or alpha is negative; an invisible value otherwise. NA values do not throw an error.

Select IG copula quantities: matching inputs

Description

The density function, 1|2 conditional cdf, and 1|2 conditional quantile function of the IG copula family. Inputs need to be vectors of the same length. These functions are called by the R functions of the same name, without the ⁠_vec⁠ suffix.

Usage

dig_vec(u, v, theta, alpha)

pcondig12_vec(u, v, theta, alpha)

qcondig12_vec(p, v, theta, alpha)

Arguments

Details

The qcondig12() function needs its own Newton Raphson algorithm. It also needs access to some version of pcondig12() and dig(). So, these three functions are coded up in C++, each with a scalar and vector pair of functions.

Note

If calling these functions manually, make sure each input are vectors of a common length.

See Also

dig(), pcondig12(), and qcondig12(); and igl_gen_vec() and family.

Send arguments to a function after vectorizing

Description

When used within a (encapsulating) function, formals_to recycles the inputs of the encapsulating function so that they are vectors of the same length, and then sends these updated arguments to some specified function.

Usage

formals_to(.fn)

Arguments

Value

The function .fn evaluated with the arguments given in the encapsulating function.

IG/IGL Generators and Related Functions: matching inputs

Description

These are the psi, H, and kappa functions of the IG and IGL copula families, but with inputs needing to be vectors of the same length. These functions are called by the R functions of the same name, without the ⁠_vec⁠ suffix.

Usage

igl_gen_vec(x, alpha)

igl_gen_D_vec(x, alpha)

igl_gen_inv_vec(p, alpha)

igl_kappa_vec(x, alpha)

igl_kappa_D_vec(x, alpha)

igl_kappa_inv_vec(p, alpha)

interp_gen_vec(x, eta, alpha)

interp_gen_inv_vec(p, eta, alpha)

interp_kappa_vec(x, eta, alpha)

interp_kappa_inv_vec(p, eta, alpha)

Arguments

Note

If calling this function manually, make sure each input are vectors of a common length.

See Also

igl_gen() and family; dig_vec(), pcondig12_vec(), and qcondig12_vec().

IG/IGL Generators and Related Functions

Description

These are the psi, H, and kappa functions of the IG and IGL copula families.

Usage

interp_gen_inv(p, eta, alpha)

interp_kappa(x, eta, alpha)

interp_kappa_inv(p, eta, alpha)

interp_gen(x, eta, alpha)

igl_kappa(x, alpha)

igl_kappa_D(x, alpha)

igl_kappa_inv(p, alpha)

igl_gen(x, alpha)

igl_gen_D(x, alpha)

igl_gen_inv(p, alpha)

Arguments

Details

Kappa function and its relatives have prefix igl_kappa; Psi function and its relatives have prefix igl_gen; Interpolating function H with either kappa or psi has igl prefix replaced with interp. Relatives of these functions: suffix inv indicates inverse; suffix D represents function derivative, and D1 derivative with respect to the first argument. . Suffix ⁠_vec⁠ indicates that the entries must be vectors of the same length; ⁠_single⁠ means entries must be scalars.

Value

The function values, as a vector.

Note

Inputs must be recyclable via vctrs::vec_recycle_common().

IG Copula Family Functions

Description

Functions related to the IG copula family, denoted by 'ig'.

Usage

pcondig21(v, u, theta, alpha)

qcondig21(p, u, theta, alpha)

qcondig(p, u, theta, alpha)

pcondig(v, u, theta, alpha)

pcondig12(u, v, theta, alpha)

qcondig12(p, v, theta, alpha)

dig(u, v, theta, alpha)

logdig(u, v, theta, alpha)

pig(u, v, theta, alpha)

rig(n, theta, alpha)

Arguments

Value

Numeric vector of length equal to the length of the input vector(s).

Note

Inputting two vectors greater than length 1 is allowed, if they're the same length. Also, qcondig21 and pcondig21 are the same as qcondig and pcondig – they're the distributions of variable 2 given 1.

Examples

u <- runif(10)
v <- runif(10)
pig(u, v, theta = 5, alpha = 1)
dig(u, v, theta = 2, alpha = 2)
logdig(u, v, theta = 2, alpha = 2)
pcondig21(v, u, theta = 3, alpha = 6)
qcondig21(v, u, theta = 3, alpha = 6)
pcondig12(u, v, theta = 3, alpha = 6)
qcondig12(u, v, theta = 3, alpha = 6)
rig(10, theta = 3, alpha = 3)

# log density available for extra precision
log(dig(0.1, 0.1, 2.5, 12.3)) == logdig(0.1, 0.1, 2.5, 12.3)

IGL Copula Family Functions

Description

Functions related to the IGL copula family, denoted by 'igl'.

Usage

qcondigl(p, u, alpha)

pcondigl(v, u, alpha)

qcondigl21(p, u, alpha)

pcondigl21(v, u, alpha)

pcondigl12(u, v, alpha)

qcondigl12(p, v, alpha)

digl(u, v, alpha)

pigl(u, v, alpha)

rigl(n, alpha)

logdigl(u, v, alpha)

Arguments

Value

Numeric vector of length equal to the length of the input vector(s).

Note

Inputting two vectors greater than length 1 is allowed, if they're the same length. Also, qcondigl21 and pcondigl21 are the same as qcondigl and pcondigl – they are the distributions of variable 2 given 1.

Examples

set.seed(1)
u <- runif(10)
v <- runif(10)
pigl(u, v, alpha = 1)
digl(u, v, alpha = 2)
logdigl(u, v, alpha = 0.4)
pcondigl21(v, u, alpha = 6)
qcondigl21(v, u, alpha = 6)
pcondigl12(u, v, alpha = 6)
qcondigl12(u, v, alpha = 6)
rigl(10, alpha = 3)