drayl_int4D {DRAYL}

Four Dimensional Rayleigh Density by Integration

Description

A four dimensional Rayleigh density by integration.

Usage

drayl_int4D(r,omega,sigma,cor,method)

Arguments

r

Evaluation point.

omega

Omega construct necessary for the Integration method.

sigma

Variances of the signals.

cor

Correlation structure.

method

Integration methods, either "Romberg","Cubature" or "Quadrature".

Value

Evaluates the 4D Rayleigh density at the point r, for the values omega,sigma and cor as specified by Bealieu's method.

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]

sigma4 = c(sqrt(c(K4[1,1],K4[3,3],K4[5,5],K4[7,7])))

cor4 = c(K4[1,3]/(sigma4[1]*sigma4[2]),
         K4[1,5]/(sigma4[1]*sigma4[3]),
         K4[1,7]/(sigma4[1]*sigma4[4]),
         K4[3,5]/(sigma4[2]*sigma4[3]),
         K4[3,7]/(sigma4[2]*sigma4[4]),
         K4[5,7]/(sigma4[3]*sigma4[4]))

omega4=omega4<-matrix(data = c(1,cor4[1],cor4[2],cor4[3],cor4[1],1,cor4[4],
                      cor4[5],cor4[2],cor4[4],1,cor4[6],cor4[3],cor4[5],cor4[6],1),nrow = 4)

drayl_int4D(c(1,1,1,1),omega = omega4,sigma = sigma4,cor = cor4, method = "Cubature")