# EstPhiNestedGumbel

    library(VecDep)

First, let us fix some parameters.

    q = 4
    dim = c(2,2)
    n = 1000

Construct a four dimensional hierarchical Gumbel copula with parameters (theta_0,theta_1,theta_2) = (2,3,4)

    hac = gethac(dim,c(2,3,4),type = 1)

Draw a sample of size n from the copula

    sample = suppressWarnings(HAC::rHAC(n,hac))
    #> [1] "X1 <-> 1"
    #> [1] "X2 <-> 2"
    #> [1] "X3 <-> 3"
    #> [1] "X4 <-> 4"

Estimate the mutual information between two random vectors of size two via pseudo maximum likelihood estimation

    estphi(sample,dim,list("hac",type = 1,M = 10000),function(t){t * log(t)})
    #> Warning in hac2nacopula(hac): NAs introduced by coercion
    #> [1] "X1 <-> 1"
    #> [1] "X2 <-> 2"
    #> [1] "X3 <-> 3"
    #> [1] "X4 <-> 4"
    #> [1] 0.4854667