docopulae (version 0.2.1)

buildf: Build Density

Description

buildf builds the joint probabilty density given the marginal distributions and some copula.

Usage

buildf(margins, copula, names = NULL)

Arguments

margins

either

• function(y, theta, ...), wherethetais a list of parameters. It shall return a column matrix of two, the probability densities and cumulative distributions.
• list of pairs of expressions, named"pdf"

copula

a copula object from package copula.

names

(if margins is a function) a vector of names or indices, the sequence of copula parameters in theta. 0 or "" indicates copula parameters to omit.

Value

• buildf returns either
  • function(y, theta, ...), the joint probability density function, ifmarginsis a function.
  • the joint probabilty density as an expression, otherwise.

Details

If buildf should build an expression, the copula shall provide distribution expressions. Please note that expressions are not validated.

References

uses substitute_q from http://adv-r.had.co.nz/Computing-on-the-language.html

See Also

copula, expr2f, numDerivLogf, DerivLogf, fisherI

Examples

## for an actual use case see examples for param

library(copula)
library(mvtnorm)

## build bivariate normal pdf
margins = function(y, theta) {
    mu = c(theta$mu1, theta$mu2)
    cbind(dnorm(y, mu), pnorm(y, mu))
}
copula = copula::normalCopula()

f = buildf(margins, copula, 'alpha')
f

## plot density
theta = list(mu1=2, mu2=-3, alpha=0.4)
y1 = seq(0, 4, length.out=51)
y2 = seq(-5, -1, length.out=51)
z = outer(y1, y2, function(y1, y2) apply(cbind(y1, y2), 1, f, theta))
contour(y1, y2, z)

## add theoretical density
copula@parameters = theta$alpha
z2 = outer(y1, y2, function(y1, y2)
    dmvnorm(cbind(y1 - theta$mu1, y2 - theta$mu2), sigma=getSigma(copula)))
contour(y1, y2, z2, col='red', add=TRUE)

## build bivariate pdf with normal margins and clayton copula
margins = list(alist(pdf=dnorm(y1, mu1, 1),
                     cdf=pnorm(y1, mu1, 1)),
               alist(pdf=dnorm(y2, mu2, 1),
                     cdf=pnorm(y2, mu2, 1)))
copula = claytonCopula()
ff = buildf(margins, copula)
f = expr2f(ff, yMap=list(y1=1, y2=2),
               thetaMap=list(mu1='mu1', mu2='mu2', alpha='alpha'))
f

margins = function(y, theta) {
    mu = c(theta$mu1, theta$mu2)
    cbind(dnorm(y, mu, 1), pnorm(y, mu, 1))
}
f2 = buildf(margins, copula, 'alpha')
f2

## plot both densities
theta = list(mu1=2, mu2=-3, alpha=2) # tau = 0.5

y1 = seq(0, 4, length.out=51)
y2 = seq(-5, -1, length.out=51)
z = outer(y1, y2, function(y1, y2) apply(cbind(y1, y2), 1, f, theta))
contour(y1, y2, z)

z2 = outer(y1, y2, function(y1, y2) apply(cbind(y1, y2), 1, f2, theta))
contour(y1, y2, z2, col='red', add=TRUE)