mvnapp: MVN Rectangle Probabilities

In weightedScores: Weighted Scores Method for Regression Models with Dependent Data

Description

Approximation to multivariate normal rectangle probabilities using methods in Joe (1995, JASA)

Usage

mvnapp(lb,ub,mu,sigma,type=1,eps=1.e-05,nsim=0)

Arguments

lb	vector of lower limits of integral/probability
ub	vector of upper limits of integral/probability
mu	mean vector
sigma	covariance matrix, it is assumed to be positive-definite
type	indicator, type=1 refers to the first order approximation, type=2 is the second order approximation.
eps	accuracy/tolerance for bivariate marginal rectangle probabilities
nsim	an optional integer if random permutations are used in the approximation for dimension >=6; nsim=2000 recommended for dim>=6

Value

prob	rectangle probability with approximation
esterr	indicator of accuracy in the approximation
ifail	= 0 if no problems >= 1 if problems from using Schervish's code in dimensions 2 to 4.

Author(s)

Harry Joe [e-mail]

References

Joe, H (1995). Approximations to multivariate normal rectangle probabilities based on conditional expectations. Journal of American Statistical Association, 90, 957–964.

Examples

m<-2
rh<-0.5
a<-c(-1,-1)
b<-c(1,1)
mu<-rep(0,m)
s<-matrix(c(1,rh,rh,1),2,2)
print(mvnapp(a,b,mu,s))
print(mvnapp(a,b,mu,s,type=2))
print(mvnapp(a,b,mu,s,type=2,nsim=3))

m<-3
rh<-0.3
a<-c(-1,-1,-2)
b<-c(1,1,.5)
mu<-rep(0,m)
s<-matrix(c(1,.5,.6,.5,1,.7,.6,.7,1),3,3)
print(mvnapp(a,b,mu,s))
print(mvnapp(a,b,mu,s,type=2))
print(mvnapp(a,b,mu,s,type=2,nsim=3))

m<-4
rh<- -0.1
a<-c(-1,-2.5,-2,-1.5)
b<-c(1.68,1.11,.5,.25)
mu<-rep(0,m)
s<-matrix(c(1,.5,.3,.4,.5,1,.5,.4,.3,.5,1,.4,.4,.4,.4,1),m,m)
print(mvnapp(a,b,mu,s))
print(mvnapp(a,b,mu,s,type=2))
print(mvnapp(a,b,mu,s,type=2,nsim=3))

m<-5
rh<-.4
a<-rep(-1,m)
b<-rep(2,m)
mu<-rep(0,m)
s<-matrix(c(1,rh,rh,rh,rh,rh,1,rh,rh,rh,rh,rh,1,rh,rh,rh,rh,rh,1,
       rh,rh,rh,rh,rh,1),m,m)
print(mvnapp(a,b,mu,s))
print(mvnapp(a,b,mu,s,type=2))
print(mvnapp(a,b,mu,s,type=2,nsim=3))

m<-6
a<-c(-1,-1,-1,-1.5,-1,-2)
b<-rep(7,m)
mu<-rep(0,m)
s<-matrix(c(1,rh,rh,rh,rh,rh,rh,1,rh,rh,rh,rh,rh,rh,1,rh,rh,rh,rh,rh,rh,1,
       rh,rh,rh,rh,rh,rh,1,rh,rh,rh,rh,rh,rh,1),m,m)
print(mvnapp(a,b,mu,s))
print(mvnapp(a,b,mu,s,type=2))
print(mvnapp(a,b,mu,s,type=2,nsim=3))

weightedScores documentation built on March 24, 2020, 1:07 a.m.