https://github.com/cran/tlmec
Tip revision: 3fc86503090bf21f2818ed8cd74acb5826736ddb authored by Larissa Matos on 01 December 2011, 00:00:00 UTC
version 0.0-2
version 0.0-2
Tip revision: 3fc8650
utils_Tstudent.R
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######################### Modelos T Mistos Censurados ##########################
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#################### Momentos da Distribuiçăo t Truncada #######################
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#GB = GenzBretz(maxpts = 1e4, abseps = 1e-9, releps = 0)
cdfNI<-function(x,mu,sigma2,nu,type="Normal"){
resp<-matrix(0,length(x),1)
if(type=="Normal"){
resp<-pnorm(x,mu,sqrt(sigma2))
}
if(type=="T"){
z=(x-mu)/sqrt(sigma2)
resp=pt(z,df=nu)
}
return(resp)
}
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#################### Momentos da Distribuiçăo t Truncada #######################
################################################################################
TT.moment = function(a,b,R,nu)
{
require(mvtnorm)
GB = GenzBretz(maxpts = 5e4, abseps = 1e-9, releps = 0)
p = length(a)
if(p==1){
if(a== -Inf) a <- -1e12
if(b== Inf) b <- 1e12
G1<- 0.5*(gamma((nu-1)/2)*nu^(nu/2))/((cdfNI(b,0,1,nu,"T")-cdfNI(a,0,1,nu,"T"))*gamma(nu/2)*gamma(1/2))
EX<- ((G1*((nu+a^2)^(-(nu-1)/2)-(nu+b^2)^(-(nu-1)/2))))
EXX<- nu/(nu-2)+(G1*(a*(nu+a^2)^(-(nu-1)/2)-b*(nu+b^2)^(-(nu-1)/2)))
}
else{
a = ifelse(a==-Inf,rep(-1e12,p),a)
b = ifelse(b== Inf,rep( 1e12,p),b)
al0 = pmvt(lower = a, upper = b, sigma = R, df = nu, algorithm = GB)[1]
### pdf & cdf
la1 = (nu-2)/nu; la2 = (nu-4)/nu
da = (nu-1)/(nu+a^2); db = (nu-1)/(nu+b^2)
f1a = sqrt(la1)*dt(sqrt(la1)*a,df=nu-2)
f1b = sqrt(la1)*dt(sqrt(la1)*b,df=nu-2)
f2 = matrix(NA, p, p)
G1a = G1b = rep(NA, p)
G2 = matrix(NA, p, p)
H = matrix(0,p,p)
for(r in 1:(p-1))
{
temp = R[-r,r]
S1 = R[-r,-r] - temp %*% t(R[r,-r])
mua = temp * a[r]; low = a[-r]-mua; upp = b[-r]-mua
G1a[r] = ifelse(p==2,pt(upp/sqrt(S1/da[r]),df=nu-1)-pt(low/sqrt(S1/da[r]),df=nu-1)
,pmvt(lower = low, upper = upp, sigma = S1/da[r], df = nu-1, algorithm = GB)[1])
mub = temp * b[r]; low = a[-r]-mub; upp = b[-r]-mub
G1b[r] = ifelse(p==2,pt(upp/sqrt(S1/db[r]),df=nu-1)-pt(low/sqrt(S1/db[r]),df=nu-1)
,pmvt(lower = low, upper = upp, sigma = S1/db[r], df = nu-1, algorithm = GB)[1])
for(s in (r+1):p)
{
rs = c(r,s)
pdf.aa = dmvt(c(a[r],a[s]),sigma=R[rs,rs]/la2,df=nu-4, log =F)
pdf.ab = dmvt(c(a[r],b[s]),sigma=R[rs,rs]/la2,df=nu-4, log =F)
pdf.ba = dmvt(c(b[r],a[s]),sigma=R[rs,rs]/la2,df=nu-4, log =F)
pdf.bb = dmvt(c(b[r],b[s]),sigma=R[rs,rs]/la2,df=nu-4, log =F)
if(p==2){cdf.aa=cdf.ab=cdf.ba=cdf.bb=1}
if(p>2)
{
tmp = R[-rs,rs]%*%solve(R[rs,rs])
mu.aa = c(tmp%*%c(a[r],a[s]))
mu.ab = c(tmp%*%c(a[r],b[s]))
mu.ba = c(tmp%*%c(b[r],a[s]))
mu.bb = c(tmp%*%c(b[r],b[s]))
daa = (nu-2)/(nu+(a[r]^2-2*R[r,s]*a[r]*a[s]+a[s]^2)/(1-R[r,s]^2))
dab = (nu-2)/(nu+(a[r]^2-2*R[r,s]*a[r]*b[s]+b[s]^2)/(1-R[r,s]^2))
dba = (nu-2)/(nu+(b[r]^2-2*R[r,s]*b[r]*a[s]+a[s]^2)/(1-R[r,s]^2))
dbb = (nu-2)/(nu+(b[r]^2-2*R[r,s]*b[r]*b[s]+b[s]^2)/(1-R[r,s]^2))
R21 = R[-rs,-rs] - R[-rs,rs]%*%solve(R[rs,rs]) %*% R[rs,-rs]
cdf.aa = ifelse(p==3,pt((b[-rs]-mu.aa)/sqrt(R21/daa),df=nu-2)-pt((a[-rs]-mu.aa)/sqrt(R21/daa),df=nu-2)
,pmvt(lower = a[-rs]-mu.aa, upper = b[-rs]-mu.aa, sigma = R21/daa, df=nu-2, algorithm = GB)[1])
cdf.ab = ifelse(p==3,pt((b[-rs]-mu.ab)/sqrt(R21/dab),df=nu-2)-pt((a[-rs]-mu.ab)/sqrt(R21/dab),df=nu-2)
,pmvt(lower = a[-rs]-mu.ab, upper = b[-rs]-mu.ab, sigma = R21/dab, df=nu-2, algorithm = GB)[1])
cdf.ba = ifelse(p==3,pt((b[-rs]-mu.ba)/sqrt(R21/dba),df=nu-2)-pt((a[-rs]-mu.ba)/sqrt(R21/dba),df=nu-2)
,pmvt(lower = a[-rs]-mu.ba, upper = b[-rs]-mu.ba, sigma = R21/dba, df=nu-2, algorithm = GB)[1])
cdf.bb = ifelse(p==3,pt((b[-rs]-mu.bb)/sqrt(R21/dbb),df=nu-2)-pt((a[-rs]-mu.bb)/sqrt(R21/dbb),df=nu-2)
,pmvt(lower = a[-rs]-mu.bb, upper = b[-rs]-mu.bb, sigma = R21/dbb, df=nu-2, algorithm = GB)[1])
}
H[r,s] = H[s,r] = pdf.aa*cdf.aa - pdf.ab*cdf.ab - pdf.ba*cdf.ba + pdf.bb*cdf.bb
}
}
##last part do loop
r <- p
temp = R[-r,r]
S1 = R[-r,-r] - temp %*% t(R[r,-r])
mua = temp * a[r]; low = a[-r]-mua; upp = b[-r]-mua
G1a[r] = ifelse(p==2,pt(upp/sqrt(S1/da[r]),df=nu-1)-pt(low/sqrt(S1/da[r]),df=nu-1)
,pmvt(lower = low, upper = upp, sigma = S1/da[r], df = nu-1, algorithm = GB)[1])
mub = temp * b[r]; low = a[-r]-mub; upp = b[-r]-mub
G1b[r] = ifelse(p==2,pt(upp/sqrt(S1/db[r]),df=nu-1)-pt(low/sqrt(S1/db[r]),df=nu-1)
,pmvt(lower = low, upper = upp, sigma = S1/db[r], df = nu-1, algorithm = GB)[1])
qa = f1a*G1a; qb = f1b*G1b
EX = c(R %*% (qa-qb)) / al0 / la1
H = H / la2
D = matrix(0,p,p)
diag(D) = a * qa - b * qb - diag(R%*%H)
al1 = pmvt(lower = a, upper = b, sigma = R/la1, df=nu-2, algorithm = GB)[1]
EXX = (al1 * R + R %*% (H + D) %*% R) / al0 / la1
}
return(list(EX=EX,EXX=EXX))
}
##Calculate the first to moments when mu not 0 and Sigma not R
Mtmvt <- function(mu,Sigma,nu,lower,upper){
p=length(lower)
if(p==1){
if(lower== -Inf) lower <- -1e12
if(upper== Inf) upper <- 1e12
a1<-(lower-mu)/sqrt(Sigma)
b1<-(upper-mu)/sqrt(Sigma)
M <- TT.moment(a1, b1, 1, nu)
Ey<- mu+sqrt(Sigma)*M$EX
Eyy<- mu^2+Sigma*M$EXX+2*mu*sqrt(Sigma)*M$EX
Vary<- Eyy - Ey^2
}
else{
Lambda <- diag(1/sqrt(diag(Sigma)))
if(length(which(upper == Inf)) != 0) upper[which(upper == Inf)] <- 1e12
b <- as.vector(diag(1/sqrt(diag(Sigma))) %*% (upper - mu))
if(length(which(lower == -Inf)) != 0) lower[which(lower == -Inf)] <- -1e12
a <- as.vector(diag(1/sqrt(diag(Sigma))) %*% (lower - mu))
R <- Lambda %*% Sigma %*% Lambda
M <- TT.moment(a, b, R, nu)
Ey <- mu + solve(Lambda) %*% M$EX
Eyy <- mu %*% t(mu) + solve(Lambda) %*% M$EX %*% t(mu) + mu %*% t(M$EX) %*% solve(Lambda) + solve(Lambda) %*% M$EXX %*% solve(Lambda)
Vary<- Eyy- Ey%*%t(Ey)
}
return(list(Ey=Ey,Eyy=Eyy,Vary=Vary))
}