drayl_int3D {DRAYL} R Documentation

## Three Dimensional Rayleigh Density by Integration

### Description

A three dimensional Rayleigh density by integration.

### Usage

drayl_int3D(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 "Kronrod","Clenshaw","Simpson","Romberg","TOMS614" or "mixed".

### Value

Evaluates the 3D Rayleigh density at the point r, for the values omega,sigma and cor as specified by Bealieu's method.

### Examples

# Matrix
K3 = matrix(0,nrow = 6,ncol = 6)
sigma3 = sqrt(c(0.5,1,1.5))
diag(K3) = c(0.5,0.5,1,1,1.5,1.5)

# rho_12 rho_13 rho_23
rho3<-c(0.9,0.8,0.7)

K3[1,3]=K3[3,1]=K3[2,4]=K3[4,2]=sigma3*sigma3*rho3
K3[1,5]=K3[5,1]=K3[2,6]=K3[6,2]=sigma3*sigma3*rho3
K3[3,5]=K3[5,3]=K3[4,6]=K3[6,4]=sigma3*sigma3*rho3

cor3 = rho3

mat<-diag(3)
mat[1,2]=mat[2,1]=cor3
mat[1,3]=mat[3,1]=cor3
mat[2,3]=mat[3,2]=cor3

omega3=mat

drayl_int3D(c(1,1,1),omega = omega3,sigma = sigma3,cor = cor3, method = "Romberg")



[Package DRAYL version 1.0 Index]