R: Various Goodness-of-fit Test Statistics

gofOtherTstat {copula} | R Documentation

## Various Goodness-of-fit Test Statistics

### Description

`gofBTstat()` computes supposedly Beta distributed test statistics for checking uniformity of `u` on the unit sphere.

### Usage

    gofBTstat(u)

### Arguments

`u` | (n,d)-matrix of values whose rows supposedly follow a uniform distribution on the unit sphere in IR^d.

### Value

An (n,d-1)-`matrix` where the (i,k)th entry is

B[ik] = (u[i,1]^2+..+u[i,k]^2) / (u[i,1]^2+..+u[i,d]^2).

### References

Li, R.-Z., Fang, K.-T., and Zhu, L.-X. (1997). Some Q-Q probability plots to test spherical and elliptical symmetry. Journal of Computational and Graphical Statistics 6(4), 435–450.

### Examples

    ## generate data on the unit sphere
    n <- 360
    d <- 5
    set.seed(1)
    x <- matrix(rnorm(n*d), ncol=d)
    U <- x/sqrt(rowSums(x^2))

    ## compute the test statistics B_k, k in {1,..,d-1}
    Bmat <- gofBTstat(U)

    ## (graphically) check if Bmat[,k] follows a Beta(k/2, (d-k)/2) distribution
    qqp <- function(k, Bmat) {
        d <- ncol(Bmat)+1L
        tit <- substitute(plain("Beta")(.A.,.B.)~~ bold("Q-Q Plot"),
                          list(.A. = k/2, .B. = (d-k)/2))
        qqplot2(Bmat[,k], qF=function(p) qbeta(p, shape1=k/2, shape2=(d-k)/2),
                main.args=list(text=tit, side=3, cex=1.3, line=1.1, xpd=NA))
    }
    qqp(1, Bmat=Bmat) # k=1
    qqp(3, Bmat=Bmat) # k=3

[Package copula version 1.0-1 Index]