dmvss | R Documentation |
Computes the the density function of the multivariate subgaussian stable distribution for arbitrary alpha, shape matrices, and location vectors. See Nolan (2013).
dmvss(
x,
alpha = 1,
Q = NULL,
delta = rep(0, d),
outermost.int = c("stats::integrate", "cubature::adaptIntegrate")[1],
spherical = FALSE,
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,
which.stable = c("libstable4u", "stabledist")[1]
)
x |
vector of quantiles. |
alpha |
default to 1 (Cauchy). Must be 0<alpha<2 |
Q |
Shape matrix. See Nolan (2013). |
delta |
location vector |
outermost.int |
select which integration function to use for outermost
integral. Default is "stats::integrate" and one can specify the following options
with the |
spherical |
default is FALSE. If true, use the spherical transformation. Results will be identical to spherical = FALSE but may be faster. |
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 |
which.stable |
defaults to "libstable4u", other option is "stabledist". Indicates which package should provide the univariate stable distribution in this production distribution form of a univariate stable and multivariate normal. |
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.
Nolan, John P. "Multivariate elliptically contoured stable distributions: theory and estimation." Computational Statistics 28.5 (2013): 2067-2089.
## print("mvsubgaussPD (d=2, alpha=1.71):")
Q <- matrix(c(10,7.5,7.5,10),2)
mvpd::dmvss(x=c(0,1), alpha=1.71, Q=Q)
## more accuracy = longer runtime
mvpd::dmvss(x=c(0,1),alpha=1.71, Q=Q, abs.tol=1e-8)
Q <- matrix(c(10,7.5,7.5,7.5,10,7.5,7.5,7.5,10),3)
## print("mvsubgausPD (d=3, alpha=1.71):")
mvpd::dmvss(x=c(0,1,2), alpha=1.71, Q=Q)
mvpd::dmvss(x=c(0,1,2), alpha=1.71, Q=Q, spherical=TRUE)
## How `delta` works: same as centering
X <- c(1,1,1)
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::dmvss(X-D, alpha=1.71, Q=Q)
mvpd::dmvss(X , alpha=1.71, Q=Q, delta=D)
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