R: Pairwise Thetas of Nested Archimedean Copulas

nacPairthetas {copula} | R Documentation

## Pairwise Thetas of Nested Archimedean Copulas

### Description

Return a d * d matrix of pairwise thetas for a nested Archimedean copula (`nacopula`) of dimension d.

### Usage

    nacPairthetas(x)

### Arguments

`x` | an (outer) nacopula (with thetas sets).

### Value

a (d x d) matrix of thetas, say `T`, where `T[j,k]` = theta of the bivariate Archimedean copula C(U_j,U_k).

### See Also

the class `nacopula` (with its `dim` method).

### Examples

    ## test with
    options(width=97)

    (mm <- rnacModel("Gumbel", d=15, pr.comp = 0.25, order="random"))
    stopifnot(isSymmetric(PT <- nacPairthetas(mm)))
    round(PT, 2)

    ## The tau's -- "Kendall's correlation matrix" :
    round(copGumbel@tau(PT), 2)

    ## do this several times:
    m1 <- rnacModel("Gumbel", d=15, pr.comp = 1/8, order="seq")
    stopifnot(isSymmetric(PT <- nacPairthetas(m1)))
    m1; PT

    m100 <- rnacModel("Gumbel", d= 100, pr.comp = 1/16, order="seq")
    system.time(PT <- nacPairthetas(m100))# how slow {non-optimal algorithm}?
    ##-- very fast, still!
    stopifnot(isSymmetric(PT))
    m100

    ## image(PT)# not ok -- want one color per theta
    nt <- length(th0 <- unique(sort(PT[!is.na(PT)])))
    th1 <- c(th0[1]/2, th0, 1.25*th0[nt])
    ths <- (th1[-1]+th1[-(nt+2)])/2
    image(log(PT), breaks = ths, col = heat.colors(nt))

    ## Nicer and easier:
    require(Matrix)
    image(as(log(PT),"Matrix"), main = "log( nacPairthetas( m100 ))",
          useAbs=FALSE, useRaster=TRUE, border=NA)

[Package copula version 1.0-1 Index]