rgnvmix | R Documentation |
Generate vectors of random variates from grouped normal variance mixtures (including Student t with multiple degrees-of-freedom).
rgnvmix(n, qmix, groupings = 1:d, loc = rep(0, d), scale = diag(2),
factor = NULL, method = c("PRNG", "sobol", "ghalton"), skip = 0, ...)
rgStudent(n, groupings = 1:d, df, loc = rep(0, d), scale = diag(2),
factor = NULL, method = c("PRNG", "sobol", "ghalton"), skip = 0)
n |
sample size |
qmix |
specification of the mixing variables |
groupings |
|
df |
|
loc |
see |
scale |
see |
factor |
see |
method |
see |
skip |
see |
... |
additional arguments (for example, parameters) passed to
the underlying mixing distribution when |
Internally used is factor
, so scale
is not required
to be provided if factor
is given.
The default factorization used to obtain factor
is the Cholesky
decomposition via chol()
. To this end, scale
needs to have full rank.
rgStudent()
is a wrapper of
rgnvmix(, qmix = "inverse.gamma", df = df)
.
rgnvmix()
returns an (n, d)
-matrix
containing n
samples of the specified (via qmix
)
d
-dimensional grouped normal variance mixture with
location vector loc
and scale matrix scale
(a covariance matrix).
rgStudent()
returns samples from the d
-dimensional
multivariate t distribution with multiple degrees-of-freedom
specified by df
, location vector
loc
and scale matrix scale
.
Erik Hintz, Marius Hofert and Christiane Lemieux
Hintz, E., Hofert, M. and Lemieux, C. (2020), Grouped Normal Variance Mixtures. Risks 8(4), 103.
Hintz, E., Hofert, M. and Lemieux, C. (2021), Normal variance mixtures: Distribution, density and parameter estimation. Computational Statistics and Data Analysis 157C, 107175.
Hintz, E., Hofert, M. and Lemieux, C. (2022), Multivariate Normal Variance Mixtures in R: The R Package nvmix. Journal of Statistical Software, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v102.i02")}.
McNeil, A. J., Frey, R. and Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques, Tools. Princeton University Press.
rnvmix()
, pgnvmix()
n <- 1000 # sample size
## Generate a random correlation matrix in d dimensions
d <- 2
set.seed(157)
A <- matrix(runif(d * d), ncol = d)
scale <- cov2cor(A %*% t(A))
## Example 1: Exponential mixture
## Let W_1 ~ Exp(1), W_2 ~ Exp(10)
rates <- c(1, 10)
#qmix <- list(list("exp", rate = rates[1]), list("exp", rate = rates[2]))
qmix <- lapply(1:2, function(i) list("exp", rate = rates[i]))
set.seed(1)
X.exp1 <- rgnvmix(n, qmix = qmix, scale = scale)
## For comparison, consider NVM distribution with W ~ Exp(1)
set.seed(1)
X.exp2 <- rnvmix(n, qmix = list("exp", rate = rates[1]), scale = scale)
## Plot both samples with the same axes
opar <- par(no.readonly = TRUE)
par(mfrow=c(1,2))
plot(X.exp1, xlim = range(X.exp1, X.exp2), ylim = range(X.exp1, X.exp2),
xlab = expression(X[1]), ylab = expression(X[2]))
mtext("Two groups with rates 1 and 10")
plot(X.exp2, xlim = range(X.exp1, X.exp2), ylim = range(X.exp1, X.exp2),
xlab = expression(X[1]), ylab = expression(X[2]))
mtext("One group with rate 1")
par(opar)
## Example 2: Exponential + Inverse-gamma mixture
## Let W_1 ~ Exp(1), W_2 ~ IG(1.5, 1.5) (=> X_2 ~ t_3 marginally)
df <- 3
qmix <- list(list("exp", rate = rates[1]),
function(u, df) 1/qgamma(1-u, shape = df/2, rate = df/2))
set.seed(1)
X.mix1 <- rgnvmix(n, qmix = qmix, scale = scale, df = df)
plot(X.mix1, xlab = expression(X[1]), ylab = expression(X[2]))
## Example 3: Mixtures in d > 2
d <- 5
set.seed(157)
A <- matrix(runif(d * d), ncol = d)
scale <- cov2cor(A %*% t(A))
## Example 3.1: W_i ~ Exp(i), i = 1,...,d
qmix <- lapply(1:d, function(i) list("exp", rate = i))
set.seed(1)
X.mix2 <- rgnvmix(n, qmix = qmix, scale = scale)
## Example 3.2: W_1, W_2 ~ Exp(1), W_3, W_4, W_5 ~ Exp(2)
## => 2 groups, so we need two elements in 'qmix'
qmix <- lapply(1:2, function(i) list("exp", rate = i))
groupings <- c(1, 1, 2, 2, 2)
set.seed(1)
X.mix3 <- rgnvmix(n, qmix = qmix, groupings = groupings, scale = scale)
## Example 3.3: W_1, W_3 ~ IG(1, 1), W_2, W_4 ~ IG(2, 2), W_5 = 1
## => X_1, X_3 ~ t_2; X_2, X_4 ~ t_4, X_5 ~ N(0, 1)
qmix <- list(function(u, df1) 1/qgamma(1-u, shape = df1/2, rate = df1/2),
function(u, df2) 1/qgamma(1-u, shape = df2/2, rate = df2/2),
function(u) rep(1, length(u)))
groupings = c(1, 2, 1, 2, 3)
df = c(2, 4, Inf)
set.seed(1)
X.t1 <- rgnvmix(n, qmix = qmix, groupings = groupings, scale = scale,
df1 = df[1], df2 = df[2])
## This is equivalent to calling 'rgnmvix' with 'qmix = "inverse.gamma"'
set.seed(1)
X.t2 <- rgnvmix(n, qmix = "inverse.gamma", groupings = groupings, scale = scale,
df = df)
## Alternatively, one can use the user friendly wrapper 'rgStudent()'
set.seed(1)
X.t3 <- rgStudent(n, df = df, groupings = groupings, scale = scale)
stopifnot(all.equal(X.t1, X.t2), all.equal(X.t1, X.t3))
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