Mvdc: Multivariate Distributions Constructed from Copulas

Description

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

For likelihood and fitting these distributions to data, see fitMvdc.

Usage

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

Value

mvdc() constructs an object of class "mvdc".

dMvdc() gives the density, pMvdc() gives the cumulative distribution function, and rMvdc() generates random variates.

Arguments

copula: an object of "copula".
margins: a character vector specifying all the parametric 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 numeric vector of length the copula dimension, say \(d\), or a matrix with the number of columns being \(d\), 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

    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.

Examples

Run this code

## 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))
# \dontshow{
set.seed(101)
# }
# 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
stopifnot(all.equal(px, pp, tolerance = 0.08))