FactorCopula (version 0.9.3)

pbnorm: Bivariate normal and Student cdfs with vectorized inputs

Description

Bivariate normal and Student cdfs with vectorized inputs

Usage

pbnorm(z1,z2,rho,icheck=FALSE)
pbvt(z1,z2,param,icheck=FALSE)

Value

cdf value(s)

Arguments

z1

scalar or vector of reals

z2

scalar or vector of reals

rho

scalar or vector parameter in (-1,1); vectors cannot have different lengths if larger than 1, each of z1,z2,rho either has length 1 or a constant n greater than 1

param

vector of length 2, or matrix with 2 columns; vectors and number of rows of matrix cannot be different if larger than 1; for param, first column is rho, second column is df.

icheck

T if checks are made for proper inputs, default of F

Details

Donnelly's code can be inaccurate in the tail when the tail probability is 2.e-9 or less (it sometimes returns 0). In the case the exchmvn code is used with dimension 2. Alternatively a user can use vectorized function pbivnorm() in the library pbivnorm, and write a function pbvncop based on it.

References

Donnelly TG (1973). Algorithm 462: bivariate normal distribution, Communications of the Association for Computing Machinery, 16, 638;

Joe H (2014) Dependence Modeling with Copulas. Chapman & Hall/CRC.

Joe H (2014) CopulaModel: Dependence Modeling with Copulas. Software for book: Dependence Modeling with Copulas, Chapman & Hall/CRC, 2014.

Examples

cat("\n pbnorm rho changing\n")
z1=.3; z2=.4; rho=seq(-1,1,.1)
out1=pbnorm(z1,z2,rho)
print(cbind(rho,out1))

cat("\n pbnorm matrix inputs for z1, z2\n")
rho=.4
z1=c(-.5,.5,10.)
z2=c(-.4,.6,10.)
z1=matrix(z1,3,3)
z2=matrix(z2,3,3,byrow=TRUE)
out3=pbnorm(z1,z2,rho)
print(out3)
cdf2=rbind(rep(0,3),out3)
cdf2=cbind(rep(0,4),cdf2)
pmf=apply(cdf2,2,diff)
pmf2=apply(t(pmf),2,diff)
pmf2=t(pmf2)  # rectangle probabilities
print(pmf2)

cat("\n pbvt rho changing\n")
z1=.3; z2=.4; rho=seq(-.9,.9,.1); nu=2
param=cbind(rho,rep(nu,length(rho)))
out1=pbvt(z1,z2,param)
print(cbind(rho,out1))
cat("\n pbvt z1 changing\n")
z1=seq(-2,2,.4)
z2=.4; rho=.5; nu=2
out2=pbvt(z1,z2,c(rho,nu))
print(cbind(z1,out2))