Help for package GRIDCOPULA

Type:

Package

Title:

Bivariate Copula Functions Based on Regular Grid

Description:

Estimates grid type bivariate copula functions, calculates some association measures and provides several copula graphics.

Version:

1.1.0

License:

GPL-3

Encoding:

UTF-8

Packaged:

2025-09-12 18:56:50 UTC; rogel

RoxygenNote:

7.2.1

Imports:

Rsolnp, fields, quadprog, ggplot2, pracma, reshape2, evmix

NeedsCompilation:

Author:

Rogelio Salinas Gutiérrez

[aut, cre, cph], Angélica Hernández Quintero

[aut, cph], Pedro Abraham Montoya Calzada

[aut, cph]

Maintainer:

Rogelio Salinas Gutiérrez <rsalinas@correo.uaa.mx>

Repository:

CRAN

Date/Publication:

2025-09-13 22:40:12 UTC

Calculates the Akaike Information Criterion "AIC" of a grid type copula

Description

This function receives a grid type copula as a parameter and returns the value of the AIC.

Usage

aic.grid(gc)

Arguments

gc

a grid type copula object.

Value

Returns a number with the AIC of a grid type copula.

Examples

# Generating simulated data with a transformation to the copula domain 
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
aic.grid(copula.grid)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
aic.grid(copula.grid)

Calculates the Bayesian Information "BIC" of a grid type copula

Description

This function receives a grid type copula as a parameter and returns the value of the BIC.

Usage

bic.grid(gc)

Arguments

gc

a grid type copula object.

Value

Returns a number with the BIC of a grid type copula.

Examples

# Generating simulated data with a transformation to the copula domain 
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
bic.grid(copula.grid)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
bic.grid(copula.grid)

Draws the density / distribution function of a grid copula with contours and colors

Description

Draws the density / distribution function of a grid copula with contours and colors

Usage

  contour_grid(gc,
  FUN = "d.grid",
  color.name = "none",
  color.size = 7,
  show.points = FALSE,
  copula.domain = TRUE,
  normal.marginal = TRUE)

Arguments

gc

a grid type copula object.

FUN

the name of the function to be applied (d.grid for density, p.grid for distribution), default is 'd.grid'.

color.name

indicates the palette of colors

color.size

indicates the number of colors.

show.points

a logical value indicating if the data must be showed or not, default is FALSE.

copula.domain

Indicates whether it is going to be graphed in the domain of the copulas U(0,1) or in the domain of the original of the variables.

normal.marginal

Indicates whether the marginals should be taken as normal distributions. The default value is TRUE, otherwise the gaussian kernel is used as marginal distribution. This argument is neccesary only if the argument copula.domain is FALSE.

Value

Returns a graph of the density / distribution.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
copula.grid <- estimate.gridCopula(U = df, k = k, m = m , method = "ml")
contour_grid(gc = copula.grid, FUN = 'd.grid', color.name = "rainbow")
contour_grid(gc = copula.grid, FUN = 'p.grid', color.name = "rainbow")

#Iris
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = k, m = m , method = "ls")
contour_grid(gc = copula.grid, FUN = 'd.grid', color.name= "rainbow",
color.size = 10, copula.domain=FALSE)
contour_grid(gc = copula.grid, FUN = 'p.grid', color.name = "rainbow",
color.size = 10, copula.domain=FALSE)

Draws the density / distribution function of a grid copula with contours and colors

Description

Draws the density / distribution function of a grid copula with contours and colors

Usage

contour_image_grid(
  gc,
  FUN = "p.grid",
  u1 = seq(0, 1, length.out = 100),
  u2 = seq(0, 1, length.out = 100),
  color.name = "heat.colors",
  color.size = 40
)

Arguments

gc

a grid type copula object.

FUN

the name of the function to be applied (d.grid, p.grid), default is 'p.grid'.

u1

indicates the place for lines on axis u_1.

u2

indicates the place for lines on axis u_2.

color.name

indicates the palette of colors.

color.size

indicates the number of colors.

Value

Returns a graph of the density / distribution.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
copula.grid <- estimate.gridCopula(U = df, k = k, m = m , method = "ls")
contour_image_grid(gc = copula.grid, FUN = 'd.grid', color.name= "rainbow", color.size = 10)
contour_image_grid(gc = copula.grid, FUN = 'p.grid', color.name = "rainbow", color.size = 10)

#Iris
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = k, m = m , method = "ls")
contour_image_grid(gc = copula.grid, FUN = 'd.grid', color.name= "rainbow", color.size = 10)
contour_image_grid(gc = copula.grid, FUN = 'p.grid', color.name = "rainbow", color.size = 10)

Evaluates the density of a grid type copula

Description

Returns the corresponding density values of a grid type copula.

Usage

d.grid(U, V = NULL, gc)

Arguments

U

a matrix of size nx2 with the observed values. It can also be a vector of size kx1 with the values of the U_1 variable.

V

optional, a vector of size kx1 with the values of the U_2 variable.

gc

a grid type copula object.

Value

Returns a vector with the corresponding density.

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
d.grid(df,gc=copula.grid)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
d.grid(copula.grid$U,gc=copula.grid)

Draws the scatter plot of bivariate data in the unit square

Description

Draws the scatter plot of bivariate data in the unit square

Usage

data.grid(U, draw.lines = TRUE, k = 4, m = 4)

Arguments

U

matrix of size kx2 with the values of both variables.

draw.lines

draws lines inside the unit square or not.

k

positive integer indicating the number of subintervals for the U_2 variable.

m

positive integer indicating the number of subintervals for the U_1 variable.

Value

Returns a scatter plot of bivariate data in the unit square.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
data.grid(U=df, draw.lines = FALSE, k = k, m = m)
data.grid(U=df, draw.lines = TRUE, k = k, m = m)

Estimates the parameters of a grid type copula

Description

This function estimates grid type copulas by one of the following methods: maximum likelihood or least squares (See reference).

Usage

estimate.gridCopula(
  X = NULL,
  U = NULL,
  k = NULL,
  m = NULL,
  method = "ml",
  D.ini = NULL,
  criterion = "AIC"
)

Arguments

X

a matrix of size nx2 with the observed values in any domain, optional if U is provided.

U

a matrix of size nx2 with the observed values in the copula domain, optional if X is provided.

k

a positive integer indicating the number of subintervals for the U_2 variable.

m

a positive integer indicating the number of subintervals for the U_1 variable.

method

The method selected for the estimation, can be least squares "ls"", maximum likelihood "ml" or penalized maximum likelihood "pml". By default "ml".

D.ini

an optional matrix with initial density values for the estimation through maximum likelihood.

criterion

If the values of k and m are not specified, they will be obtained by the "AIC" or "BIC" criteria, by default "AIC".

Value

Returns a list with a matrix with the density over the grid, a matrix with the quantity of data over the grid, the number of subintervals for the U_2 variable, the number of subintervals for the U_1 variable, a matrix with the values of u_1 and u_2 in the copula domain and a matrix with the original values X.

References

Pfeifer, D., Strassburger, D., & Philipps, J. (2020). Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas. arXiv. Retrieved from https://arxiv.org/abs/2010.15709

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
print(copula.grid$Density)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
print(copula.grid$Density)

Draws the density of a grid copula with colors

Description

Draws the density of a grid copula with colors

Usage

image_color_grid(gc, color.name = "heat.colors", color.size = 7)

Arguments

gc

a grid type copula object.

color.name

indicates the palette of colors.

color.size

indicates the number of colors.

Value

Returns a graph of the density.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
copula.grid <- estimate.gridCopula(U = df, k = k, m = m , method = "ml")
image_color_grid(gc = copula.grid, color.name = "rainbow", color.size = 10)

#Iris
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = k, m = m , method = "ml")
image_color_grid(gc = copula.grid, color.name = "rainbow", color.size = 10)

Returns dependency measures for a grid type copula

Description

Returns dependency measures for a grid type copula

Usage

measures.grid(gc, measures = "all")

Arguments

gc

a grid type copula object.

measures

A vector of the measurements to calculate: "gini", "blomqvist", "tail_U", "tail_L", "rho", "tau","mi", by default "all".

Details

"tau": Kendall's \tau, see Nelsen (2007).
"rho": Spearman's \rho, see Nelsen (2007).
"blomqvist": Blomqvist's \beta; computed as 4C(0.5, 0.5) - 1, see Nelsen (2007).
"gini": Gini's \gamma, see Nelsen (2007).
"mi": Mutual information, see Joe (1989).
"tail_U/tail_L": Tail dependency, see Nelsen (2007).

Value

A list with dependence measures

References

Nelsen, R. (2007). An introduction to copulas. Springer Science & Business Media.

Joe, H. (1989). Relative Entropy Measures of Multivariate Dependence. Journal of the American Statistical Association.

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
measures.grid(copula.grid) 
measures.grid(copula.grid, measures = c("rho","tau","mi"))

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
measures.grid(copula.grid, measures = c("gini", "blomqvist", "tail_U", "tail_L", "rho"))

Draws the density of a grid copula with mosaics

Description

Draws the density of a grid copula with mosaics

Usage

mosaic.grid(gc, number.size = 5)

Arguments

gc

a grid type copula object.

number.size

indicates the size of numbers.

Value

Returns a graph.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
copula.grid <- estimate.gridCopula(U = df, k = k, m = m , method = "ml")
mosaic.grid(gc = copula.grid, number.size = 5)

#Iris
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = k, m = m , method = "ml")
mosaic.grid(gc = copula.grid, number.size = 5)

Evaluates the distribution function of a grid type copula

Description

Returns the corresponding distribution function values.

Usage

p.grid(U, V = NULL, gc)

Arguments

U

a matrix of size nx2 with the observed values. It can also be a vector of size kx1 with the values of the U_1 variable.

V

optional, a vector of size kx1 with the values of theU_2 variable.

gc

a grid type copula object.

Value

Returns a vector with the corresponding distribution.

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
p.grid(df,gc=copula.grid)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
p.grid(copula.grid$U,gc=copula.grid)

Draws the density / distribution function of a grid copula with perspective

Description

Draws the density / distribution function of a grid copula with perspective

Usage

perspective.grid(
  gc,
  FUN = "d.grid",
  u1 = seq(0, 1, length.out = 21),
  u2 = seq(0, 1, length.out = 21),
  ang.theta = -30,
  ang.phi = 25,
  distancia = 10
)

Arguments

gc

a grid type copula object.

FUN

the name of the function to be applied (d.grid, p.grid), default is 'd.grid'.

u1

indicates the place for lines on axis u_1.

u2

indicates the place for lines on axis u_2.

ang.theta

angle for the azimuthal direction.

ang.phi

angle for the colatitude.

distancia

the distance of the eyepoint from the centre of the box.

Value

Returns a graph of the density / distribution.

Examples

n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
k <- 10
m <- 10
copula.grid <- estimate.gridCopula(U = df, k = k, m = m , method = "ml")
perspective.grid(gc = copula.grid, ang.theta = 90 , ang.phi = 80, distancia = 3)
perspective.grid(gc = copula.grid, FUN = "p.grid")

#Iris 
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = k, m = m , method = "ml")
perspective.grid(gc = copula.grid, ang.theta = 90 , ang.phi = 80, distancia = 3)
perspective.grid(gc = copula.grid, FUN = "p.grid")

Generates a random sample from a grid type copula

Description

Generates a random sample from a grid type copula

Usage

r.grid(n, gc)

Arguments

n

an integer number indicating the size of the sample.

gc

a grid type copula object.

Value

Returns a matrix of size nx2 with the random sample.

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 15, m = 15 , method = "ml")
df2 <- r.grid(n = n, gc = copula.grid)
data.grid(copula.grid$U, k = 15, m = 15)
data.grid(df2, k = 15, m = 15)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
df2 <- r.grid(n = n, gc = copula.grid)
data.grid(copula.grid$U, k = 3, m = 7)
data.grid(df2, k = 3, m = 7)