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Last data update: 2014.03.03

R: Multivariate Distributions Constructed from Copulas

Mvdc	R Documentation

Multivariate Distributions Constructed from Copulas

Description

Density, distribution function, and random generator for a multivariate distribution via copula.

Usage

mvdc(copula, margins, paramMargins, marginsIdentical = FALSE,
     check = TRUE, fixupNames = TRUE)
dMvdc(x, mvdc, log=FALSE)
pMvdc(x, mvdc)
rMvdc(n, mvdc)

Arguments

`copula`	an object of `"copula"`.
`margins`	a character vector specifying all the marginal distributions. See details below.
`paramMargins`	a `list` whose each component is a list (or numeric vectors) of named components, giving the parameter values of the marginal distributions. See details below.
`marginsIdentical`	logical variable restricting the marginal distributions to be identical.
`check`	logical indicating to apply quick checks about existence of `margins` “p” and “d” functions.
`fixupNames`	logical indicating if the parameters of the margins should get automatic names (from `formals(p<mar_i>)`).
`mvdc`	a `"mvdc"` object.
`x`	a vector of the copula dimension or a matrix with number of columns being the copula dimension, giving the coordinates of the points where the density or distribution function needs to be evaluated.
`log`	logical indicating if the `log` density should be returned.
`n`	number of observations to be generated.

Details

The characters in argument margins are used to construct density, distribution, and quantile function names. For example, norm can be used to specify marginal distribution, because dnorm, pnorm, and qnorm are all available.

A user-defined distribution, for example, fancy, can be used as margin provided that dfancy, pfancy, and qfancy are available.

Each component list in argument paramMargins is a list with named components which are used to specify the parameters of the marginal distributions. For example, the list

code{paramMargins = list(list(mean = 0, sd = 2), list(rate = 2))}

can be used to specify that the first margin is normal with mean 0 and standard deviation 2, and the second margin is exponential with rate 2.

Value

mvdc() constructs an object of class "mvdc". dMvdc() gives the density, pMvdc() gives the cumulative distribution function, and rMvdc() generates random variates.

Examples

## construct a bivariate distribution whose marginals
## are normal and exponential respectively, coupled
## together via a normal copula
mv.NE <- mvdc(normalCopula(0.75), c("norm", "exp"),
              list(list(mean = 0, sd =2), list(rate = 2)))
dim(mv.NE)
mv.NE  # using its print() / show() method

persp  (mv.NE, dMvdc, xlim = c(-4, 4), ylim=c(0, 2), main = "dMvdc(mv.NE)")
persp  (mv.NE, pMvdc, xlim = c(-4, 4), ylim=c(0, 2), main = "pMvdc(mv.NE)")
contour(mv.NE, dMvdc, xlim = c(-4, 4), ylim=c(0, 2))

# Generate (bivariate) random numbers from that, and visualize
x.samp <- rMvdc(250, mv.NE)
plot(x.samp)
summary(fx <- dMvdc(x.samp, mv.NE))
summary(Fx <- pMvdc(x.samp, mv.NE))
op <- par(mfcol=c(1,2))
pp <- persp(mv.NE, pMvdc, xlim = c(-5,5), ylim=c(0,2),
            main = "pMvdc(mv.NE)", ticktype="detail")

px <- copula:::perspMvdc(x.samp, fun = F.n, xlim = c(-5,5), ylim=c(0,2),
                         main = "F.n(x.samp)", ticktype="detail")
par(op)
all.equal(px, pp)# about 5% difference