drayl4D {DRAYL}

Four dimensional Rayleigh density by series expansion

Description

Returns a 4D Rayleigh density for arbitrary covariance values. The resulting function can then be evaluated at arbitrary points.

Usage

drayl4D(dK,Ccomp,lim)

Arguments

dK

Determinant of the covariance matrix.

Ccomp

"Compressed" cofactor matrix, leaving out zero value entries.

lim

Number of series terms.

Value

The 4D Rayleigh density for the compressed cofactor matrix Ccomp of the covariance matrix. The function can then be evaluated for 4-dimensional vectors r.

Examples

library("RConics")

K4 = matrix(0,nrow = 8,ncol = 8)
sigma4 = sqrt(c(0.5,1,1.5,1))
rho4<-c(0.7,0.75,0.8,0.7,0.75,0.7)

K4[1,1]=K4[2,2]=sigma4[1]^2
K4[3,3]=K4[4,4]=sigma4[2]^2
K4[5,5]=K4[6,6]=sigma4[3]^2
K4[7,7]=K4[8,8]=sigma4[4]^2

K4[1,3]=K4[3,1]=K4[2,4]=K4[4,2]=sigma4[1]*sigma4[2]*rho4[1]
K4[1,5]=K4[5,1]=K4[2,6]=K4[6,2]=sigma4[1]*sigma4[3]*rho4[2]
K4[1,7]=K4[7,1]=K4[2,8]=K4[8,2]=sigma4[1]*sigma4[4]*rho4[3]
K4[3,5]=K4[5,3]=K4[4,6]=K4[6,4]=sigma4[2]*sigma4[3]*rho4[4]
K4[3,7]=K4[7,3]=K4[4,8]=K4[8,4]=sigma4[2]*sigma4[4]*rho4[5]
K4[5,7]=K4[7,5]=K4[8,6]=K4[6,8]=sigma4[3]*sigma4[4]*rho4[6]

C4=adjoint(K4)
n = nrow(K4)/2
Ccomp4<-C4[seq(1,(2*n-1),2),][,seq(1,(2*n-1),2)]
dK4<-det(K4)

pdf4D<-drayl4D(dK = dK4, Ccomp = Ccomp4, lim = 3)
pdf4D(rep(1,4))