drayl_int4D: Four Dimensional Rayleigh Density by Integration

In DRAYL: Computation of Rayleigh Densities of Arbitrary Dimension

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")

DRAYL documentation built on Aug. 21, 2019, 9:05 a.m.