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# $Id: mvt.R 2936 2006-09-08 11:30:57Z hothorn $
checkmvArgs <- function(lower, upper, mean, corr, sigma)
{
UNI <- FALSE
if (is.null(lower) || any(is.na(lower)))
stop(sQuote("lower"), " not specified or contains NA")
if (is.null(upper) || any(is.na(upper)))
stop(sQuote("upper"), " not specified or contains NA")
rec <- cbind(lower, upper, mean)
lower <- rec[,"lower"]
upper <- rec[,"upper"]
if (!all(lower <= upper))
stop("at least one element of ", sQuote("lower"), " is larger than ",
sQuote("upper"))
mean <- rec[,"mean"]
if (any(is.na(mean)))
stop("mean contains NA")
if (is.null(corr) && is.null(sigma)) {
corr <- diag(length(lower))
# warning("both ", sQuote("corr"), " and ", sQuote("sigma"),
# " not specified: using sigma=diag(length(lower))")
}
if (!is.null(corr) && !is.null(sigma)) {
sigma <- NULL
warning("both ", sQuote("corr"), " and ", sQuote("sigma"),
" specified: ignoring ", sQuote("sigma"))
}
if (!is.null(corr)) {
if (!is.matrix(corr)) {
if (length(corr) == 1)
UNI <- TRUE
if (length(corr) != length(lower))
stop(sQuote("diag(corr)"), " and ", sQuote("lower"),
" are of different length")
} else {
if (length(corr) == 1) {
UNI <- TRUE
corr <- corr[1,1]
if (length(lower) != 1)
stop(sQuote("corr"), " and ", sQuote("lower"),
" are of different length")
} else {
if (length(diag(corr)) != length(lower))
stop(sQuote("diag(corr)"), " and ", sQuote("lower"),
" are of different length")
}
}
}
if (!is.null(sigma)) {
if (!is.matrix(sigma)) {
if (length(sigma) == 1)
UNI <- TRUE
if (length(sigma) != length(lower))
stop(sQuote("diag(sigma)"), " and ", sQuote("lower"),
" are of different length")
} else {
if (length(sigma) == 1) {
UNI <- TRUE
sigma <- sigma[1,1]
if (length(lower) != 1)
stop(sQuote("sigma"), " and ", sQuote("lower"),
" are of different length")
} else {
if (length(diag(sigma)) != length(lower))
stop(sQuote("diag(sigma)"), " and ", sQuote("lower"),
" are of different length")
}
}
}
list(lower=lower, upper=upper, mean=mean, corr=corr, sigma=sigma, uni=UNI)
}
pmvnorm <- function(lower=-Inf, upper=Inf, mean=rep(0, length(lower)), corr=NULL, sigma=NULL,
maxpts = 25000, abseps = 0.001, releps = 0)
{
carg <- checkmvArgs(lower=lower, upper=upper, mean=mean, corr=corr,
sigma=sigma)
if (!is.null(carg$corr)) {
corr <- carg$corr
if (carg$uni) {
stop(sQuote("sigma"), " not specified: cannot compute pnorm")
} else {
lower <- carg$lower - carg$mean
upper <- carg$upper - carg$mean
mean <- rep(0, length(lower))
RET <- mvt(lower=lower, upper=upper, df=0, corr=corr, delta=mean,
maxpts=maxpts, abseps=abseps,releps=releps)
}
} else {
if (carg$uni) {
RET <- list(value = pnorm(carg$upper, mean=carg$mean, sd=sqrt(carg$sigma)) -
pnorm(carg$lower, mean=carg$mean, sd=sqrt(carg$sigma)),
error = 0, msg="univariate: using pnorm")
} else {
lower <- (carg$lower - carg$mean)/sqrt(diag(carg$sigma))
upper <- (carg$upper - carg$mean)/sqrt(diag(carg$sigma))
mean <- rep(0, length(lower))
corr <- cov2cor(carg$sigma)
RET <- mvt(lower=lower, upper=upper, df=0, corr=corr, delta=mean,
maxpts=maxpts, abseps=abseps,releps=releps)
}
}
attr(RET$value, "error") <- RET$error
attr(RET$value, "msg") <- RET$msg
return(RET$value)
}
pmvt <- function(lower=-Inf, upper=Inf, delta=rep(0, length(lower)),
df=1, corr=NULL, sigma=NULL, maxpts = 25000, abseps = 0.001,
releps = 0)
{
carg <- checkmvArgs(lower=lower, upper=upper, mean=delta, corr=corr,
sigma=sigma)
if (is.null(df))
stop(sQuote("df"), " not specified")
if (any(df < 0))
stop("cannot compute multivariate t distribution with ",
sQuote("df"), " < 0")
if (carg$uni) {
if (df > 0)
RET <- list(value = pt(carg$upper, df=df, ncp=carg$mean) -
pt(carg$lower, df=df, ncp=carg$mean),
error = 0, msg="univariate: using pt")
else
RET <- list(value = pnorm(carg$upper, mean = carg$mean) -
pnorm(carg$lower, mean=carg$mean),
error = 0, msg="univariate: using pnorm")
} else {
if (!is.null(carg$corr)) {
RET <- mvt(lower=carg$lower, upper=carg$upper, df=df, corr=carg$corr,
delta=carg$mean, maxpts=maxpts,
abseps=abseps,releps=releps)
} else {
lower <- carg$lower/sqrt(diag(carg$sigma))
upper <- carg$upper/sqrt(diag(carg$sigma))
corr <- cov2cor(carg$sigma)
RET <- mvt(lower=lower, upper=upper, df=df, corr=corr,
delta=carg$mean, maxpts=maxpts,
abseps=abseps,releps=releps)
}
}
attr(RET$value, "error") <- RET$error
attr(RET$value, "msg") <- RET$msg
return(RET$value)
}
mvt <- function(lower, upper, df, corr, delta, maxpts = 25000,
abseps = 0.001, releps = 0)
{
### handle cases where the support is the empty set
if (any(abs(lower - upper)) < sqrt(.Machine$double.eps) ||
any(is.na(lower - upper))) {
RET <- list(value = 0, error = 0, msg = "lower == upper")
return(RET)
}
n <- ncol(corr)
if (is.null(n) || n < 2) stop("dimension less then n = 2")
if (length(lower) != n) stop("wrong dimensions")
if (length(upper) != n) stop("wrong dimensions")
if (n > 1000) stop("only dimensions 1 <= n <= 1000 allowed")
infin <- rep(2, n)
infin[upper == Inf] <- 1
infin[lower == -Inf] <- 0
infin[lower == -Inf & upper == Inf] <- -1
### this is a bug in `mvtdst' not yet fixed
if (all(infin < 0))
return(list(value = 1, error = 0, msg = "Normal Completion"))
if (n > 1) {
corrF <- matrix(as.vector(corr), ncol=n, byrow=TRUE)
corrF <- corrF[upper.tri(corrF)]
} else corrF <- corr
lower[lower == -Inf] <- 0
upper[upper == Inf] <- 0
error <- 0; value <- 0; inform <- 0
### TOL argument re-added in version 0.6-3
### not yet exported
tol <- 1e-10
ret <- .Fortran("mvtdst", N = as.integer(n),
NU = as.integer(df),
LOWER = as.double(lower),
UPPER = as.double(upper),
INFIN = as.integer(infin),
CORREL = as.double(corrF),
DELTA = as.double(delta),
MAXPTS = as.integer(maxpts),
ABSEPS = as.double(abseps),
RELEPS = as.double(releps),
TOL = as.double(tol),
error = as.double(error),
value = as.double(value),
inform = as.integer(inform), PACKAGE="mvtnorm")
error <- ret$error; value <- ret$value; inform <- ret$inform
msg <- NULL
if (inform == 0) msg <- "Normal Completion"
if (inform == 1) msg <- "Completion with error > abseps"
if (inform == 2) msg <- "N greater 1000 or N < 1"
if (inform == 3) msg <- "Covariance matrix not positive semidefinite"
if (is.null(msg)) msg <- inform
RET <- list(value = value, error = error, msg = msg)
return(RET)
}
rmvt <- function(n, sigma=diag(2), df=1) {
rmvnorm(n,sigma=sigma)/sqrt(rchisq(n,df)/df)
}
dmvt <- function(x, delta, sigma, df = 1, log = TRUE)
{
if (df == 0)
return(dmvnorm(x, mean = delta, sigma = sigma, log = log))
if (is.vector(x)) {
x <- matrix(x, ncol = length(x))
}
if (missing(delta)) {
delta <- rep(0, length = ncol(x))
}
if (missing(sigma)) {
sigma <- diag(ncol(x))
}
if (NCOL(x) != NCOL(sigma)) {
stop("x and sigma have non-conforming size")
}
if (NROW(sigma) != NCOL(sigma)) {
stop("sigma meanst be a square matrix")
}
if (length(delta) != NROW(sigma)) {
stop("mean and sigma have non-conforming size")
}
m <- NCOL(sigma)
distval <- mahalanobis(x, center = delta, cov = sigma)
logdet <- sum(log(eigen(sigma, symmetric = TRUE,
only.values = TRUE)$values))
logretval <- lgamma((m + df)/2) -
(lgamma(df / 2) + 0.5 * (logdet + m * logb(pi * df))) -
0.5 * (df + m) * logb(1 + distval / df)
if (log)
return(logretval)
return(exp(logretval))
}
qmvnorm <- function(p, interval = c(-10, 10),
tail = c("lower.tail", "upper.tail", "both.tails"),
mean = 0, corr = NULL, sigma = NULL,
maxpts = 25000, abseps = 0.001, releps = 0, ...) {
if (length(p) != 1 || (p <= 0 || p >= 1))
stop(sQuote("p"), " is not a double between zero and one")
tail <- match.arg(tail)
dim <- length(mean)
if (is.matrix(corr)) dim <- nrow(corr)
if (is.matrix(sigma)) dim <- nrow(sigma)
lower <- rep(0, dim)
upper <- rep(0, dim)
args <- checkmvArgs(lower, upper, mean, corr, sigma)
dim <- length(args$mean)
pfct <- function(q) {
switch(tail, "both.tails" = {
low <- rep(-abs(q), dim)
upp <- rep( abs(q), dim)
}, "upper.tail" = {
low <- rep( q, dim)
upp <- rep( Inf, dim)
}, "lower.tail" = {
low <- rep( -Inf, dim)
upp <- rep( q, dim)
},)
pmvnorm(lower = low, upper = upp, mean = args$mean,
corr = args$corr, sigma = args$sigma,
abseps = abseps, maxpts = maxpts, releps = releps) - p
}
if (tail == "both.tails") {
interval[1] <- 0
interval <- abs(interval)
}
qroot <- uniroot(pfct, interval = interval, ...)
names(qroot)[1:2] <- c("quantile", "f.quantile")
qroot
}
qmvt <- function(p, interval = c(-10, 10),
tail = c("lower.tail", "upper.tail", "both.tails"),
df = 1, delta = 0, corr = NULL, sigma = NULL,
maxpts = 25000, abseps = 0.001, releps = 0, ...) {
if (length(p) != 1 || (p <= 0 || p >= 1))
stop(sQuote("p"), " is not a double between zero and one")
tail <- match.arg(tail)
dim <- length(mean)
if (is.matrix(corr)) dim <- nrow(corr)
if (is.matrix(sigma)) dim <- nrow(sigma)
lower <- rep(0, dim)
upper <- rep(0, dim)
args <- checkmvArgs(lower, upper, delta, corr, sigma)
dim <- length(args$mean)
pfct <- function(q) {
switch(tail, "both.tails" = {
low <- rep(-abs(q), dim)
upp <- rep( abs(q), dim)
}, "upper.tail" = {
low <- rep( q, dim)
upp <- rep( Inf, dim)
}, "lower.tail" = {
low <- rep( -Inf, dim)
upp <- rep( q, dim)
},)
pmvt(lower = low, upper = upp, df = df, delta = args$mean,
corr = args$corr, sigma = args$sigma,
abseps = abseps, maxpts = maxpts, releps = releps) - p
}
if (tail == "both.tails") {
interval[1] <- 0
interval <- abs(interval)
}
qroot <- uniroot(pfct, interval = interval, ...)
names(qroot)[1:2] <- c("quantile", "f.quantile")
qroot
}
|
