lcomCOPpv {copBasic} | R Documentation |
Simulating the Sample Distribution(s) of L-correlation, L-coskew, and L-cokurtosis for a Copula
Description
EXPERIMENTAL: The function provides two themes of sampling distribution characterization by simulation of the first three L-comoment ratios (L-correlation , L-coskew
and L-cokurtosis
) of a copula. Subsequently, the sampling distribution can be used for inference.
First, semi-optional Monte Carlo integration estimation of the L-comoments of the parent copula are computed. Second, simulations involving the sample size presumed the size of the actual sample from which the estimates of the sample L-comoments given as arguments. These simulations result in a report of the L-moments (not L-comoments) of the sampling distribution and these then are used to compute p-values for the L-comoment matrices provided by the user as a function argument.
Usage
lcomCOPpv(n, lcom, cop=NULL, para=NULL, repcoe=5E3, type="gno",
mcn=1E4, mcrep=10, usemcmu=FALSE, digits=5, ...)
Arguments
n |
The sample size |
lcom |
The sample L-comoments (see below); |
cop |
A copula function; |
para |
Vector of parameters, if needed, to pass to the copula; |
repcoe |
The replication coefficient |
type |
The distribution type used for modeling the distribution of the sampling values. The generalized normal (see distribution type |
mcn |
The sample size |
mcrep |
The number of replications of the Monte Carlo simulation by |
usemcmu |
A logical toggling whether the mean value computed from the replicated Monte Carlo integrations is used instead of the mean values for the small sample simulation for the p-value computations; |
digits |
The number of digits to round numerical entries in the returned tables and can be |
... |
Additional arguments to pass to the |
Details
The notation refers to two specific types of L-comoment definitions and a blend between the two. The notation
means that the
th L-comoment for random variables
where
is the sorted variable and
is shuffled by the sorting index. Conversely, the notation
means that the
th L-comoment for random variables
where
is the sorted variable and
is shuffled by the sorting index. The notation
means that the average between the
and
is computed, which might prove useful in circumstances of known or expected symmetry of the L-comoments.
Continuing, is the sample L-correlation,
is the sample L-coskew, and
is the sample L-cokurtosis all with respect to the sorting of the second variable. The computation of these L-comoment matricies can be made by functions such as function
lcomoms2()
in the lmomco package. The number of replications for the simulations involving the sample size is computed by
where is the
repcoe
replication factor or coefficient. If usemcmu
is TRUE
then mcn
else
usemcmu
is reset to FALSE
.
Value
An R list
is returned.
text |
A string functioning as a label for the remaining tables; |
Ntable |
Another R |
ntable |
Another R |
Note
A significance column for the p-values is added to the right side of the returned ntable
and is used to guide the eye in interpretation of results. The significant codes having the following definitions for a two-tailed form:
"_" > 0.1; ".", 0.1; "*", 0.05; "**", 0.01; "***", 0.001
Author(s)
W.H. Asquith
References
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
See Also
lcomCOP
, COP
, kullCOP
, vuongCOP
Examples
# See Note section of vuongCOP() for an extended discussion of copula inference
## Not run:
Tau <- 0.6410811; para <- GHcop(tau=Tau)$para # This Tau is from a situation of
# two river tributaries. These three L-comoments with univariate L-moments on the
T2 <- c(1, 0.79908960, 0.79908960, 1) # diagonals are derived from those river
# tributaries and downstream of the junction data.
T3 <- c(0, -0.04999318, 0.07689082, 0)
T4 <- c(0, 0.01773833, 0.04756257, 0) # Is the Ho:GHcop rejectable?
LCOM <- list(T2=matrix(T2, nrow=2), T3=matrix(T3, nrow=2), T4=matrix(T4, nrow=2))
set.seed(30312)
ZZ1 <- lcomCOPpv(75, LCOM, cop=GHcop, para=para, repcoe=2000, usemcmu=FALSE)
print(ZZ1)
set.seed(30312)
ZZ2 <- lcomCOPpv(75, LCOM, cop=GHcop, para=para, repcoe=2000, usemcmu=TRUE)
print(ZZ2)
# The results here suggest that the GHcop is not rejectable.
## End(Not run)