fact1mvn: Rectangle probability for multivariate normal with 1-factor...
In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description Usage Arguments Details Value See Also Examples

Rectangle probability for multivariate normal with 1-factor structure

1	fact1mvn(lb,ub,load1,eps=1.e-6,B=6)

`lb`	vector of lower limits of integral/probability
`ub`	vector of upper limits of integral/probability
`load1`	loading vector for factor 1
`eps`	tolerance for numerical integration
`B`	upper limit of integration and negative of lower limit

For the 1-factor dxd correlation structure, the rectangle probability is a 1-dimensional integral. The positive exchangeable correlation matrix is a special case.

rectangle probability

exchmvn

d=5
lb=rep(-1,d)
ub=c(2,1.5,1,1.5,2)
rho=.6
pr=exchmvn(lb,ub,rho)
cat("pr=exchmvn(lb,ub,rho)=",pr,"\n")
load1=rep(sqrt(rho),d)
pr2=fact1mvn(lb,ub,load1)
cat("pr=fact1mvn(lb,ub,load1)=",pr2,"\n")
# higher-dimensional example
load=c(.9,.8,.2,.2,.2,.2,.2,.2)
d=length(load)
uvec=seq(.3,.9,.2)
for(i in 1:length(uvec)) 
{ y=qnorm(uvec[i])
  jcdf=fact1mvn(rep(-6,d),rep(y,d),load)
  cat(y,jcdf,"\n")
}