pmvlogis {mvpd} | R Documentation |
Multivariate Elliptically Contoured Logistic Distribution
Description
Computes the probabilities for the multivariate elliptically contoured distribution for arbitrary limits, shape matrices, and location vectors.
Usage
pmvlogis(
lower = rep(-Inf, d),
upper = rep(Inf, d),
nterms = 500,
Q = NULL,
delta = rep(0, d),
maxpts.pmvnorm = 25000,
abseps.pmvnorm = 0.001,
outermost.int = c("stats::integrate", "cubature::adaptIntegrate")[1],
subdivisions.si = 100L,
rel.tol.si = .Machine$double.eps^0.25,
abs.tol.si = rel.tol.si,
stop.on.error.si = TRUE,
tol.ai = 1e-05,
fDim.ai = 1,
maxEval.ai = 0,
absError.ai = 0,
doChecking.ai = FALSE
)
Arguments
lower |
the vector of lower limits of length n. |
upper |
the vector of upper limits of length n. |
nterms |
the number of terms in the limiting form's sum. That is, changing the infinity on the top of the summation to a big K. This is an argument passed to dkolm(). |
Q |
Shape matrix. See Nolan (2013). |
delta |
location vector. |
maxpts.pmvnorm |
Defaults to 25000. Passed to the F_G = pmvnorm() in the integrand of the outermost integral. |
abseps.pmvnorm |
Defaults to 1e-3. Passed to the F_G = pmvnorm() in the integrand of the outermost integral. |
outermost.int |
select which integration function to use for outermost
integral. Default is "stats::integrate" and one can specify the following options
with the |
subdivisions.si |
the maximum number of subintervals.
The suffix |
rel.tol.si |
relative accuracy requested.
The suffix |
abs.tol.si |
absolute accuracy requested. The suffix |
stop.on.error.si |
logical. If true (the default) an error stops the function.
If false some errors will give a result with a warning in the message component.
The suffix |
tol.ai |
The maximum tolerance, default 1e-5.
The suffix |
fDim.ai |
The dimension of the integrand, default 1, bears no
relation to the dimension of the hypercube
The suffix |
maxEval.ai |
The maximum number of function evaluations needed,
default 0 implying no limit
The suffix |
absError.ai |
The maximum absolute error tolerated
The suffix |
doChecking.ai |
A flag to be thorough checking inputs to
C routines. A FALSE value results in approximately 9 percent speed
gain in our experiments. Your mileage will of course vary. Default
value is FALSE.
The suffix |
Value
The object returned depends on what is selected for outermost.int
. In the case of the default,
stats::integrate
, the value is a list of class "integrate" with components:
value |
the final estimate of the integral. |
abs.error |
estimate of the modulus of the absolute error. |
subdivisions |
the number of subintervals produced in the subdivision process. |
message |
"OK" or a character string giving the error message. |
call |
the matched call. |
Note: The reported abs.error
is likely an under-estimate as integrate
assumes the integrand was without error,
which is not the case in this application.
References
Nolan JP (2013), Multivariate elliptically contoured stable distributions: theory and estimation. Comput Stat (2013) 28:2067–2089 DOI 10.1007/s00180-013-0396-7
Examples
## bivariate
U <- c(1,1)
L <- -U
Q <- matrix(c(10,7.5,7.5,10),2)
mvpd::pmvlogis(L, U, nterms=1000, Q=Q)
## trivariate
U <- c(1,1,1)
L <- -U
Q <- matrix(c(10,7.5,7.5,7.5,10,7.5,7.5,7.5,10),3)
mvpd::pmvlogis(L, U, nterms=1000, Q=Q)
## How `delta` works: same as centering
U <- c(1,1,1)
L <- -U
Q <- matrix(c(10,7.5,7.5,7.5,10,7.5,7.5,7.5,10),3)
D <- c(0.75, 0.65, -0.35)
mvpd::pmvlogis(L-D, U-D, nterms=100, Q=Q)
mvpd::pmvlogis(L , U , nterms=100, Q=Q, delta=D)
## recover univariate from trivariate
crit_val <- -1.3
Q <- matrix(c(10,7.5,7.5,7.5,20,7.5,7.5,7.5,30),3) / 10
Q
pmvlogis(c(-Inf,-Inf,-Inf),
c( Inf, Inf, crit_val),
Q=Q)
plogis(crit_val, scale=sqrt(Q[3,3]))
pmvlogis(c(-Inf, -Inf,-Inf),
c( Inf, crit_val, Inf ),
Q=Q)
plogis(crit_val, scale=sqrt(Q[2,2]))
pmvlogis(c( -Inf, -Inf,-Inf),
c( crit_val, Inf, Inf ),
Q=Q)
plogis(crit_val, scale=sqrt(Q[1,1]))