uvlmoms {copBasic} | R Documentation |
Bivariate Skewness after Joe (2014) or the Univariate L-moments of Combined U and V
Description
Joe (2014, pp. 65–66) suggests two quantile-based measures of bivariate skewness defined for uniform random variables and
combined as either
or
for which the
. The bivariate skewness is the quantity
:
where ,
is the quantile function for nonexceedance probability
for either the quantities
or
using either the empirical quantile function or a fitted distribution. Joe (2014, p. 66) reports that
to “achieve some sensitivity to the tails.” How these might be related (intuitively) to L-coskew (see function
lcomoms2()
of the lmomco package) of the L-comoments or bivariate L-moments (bilmoms
) is unknown, but see the Examples section of joeskewCOP
.
Structurally the above definition for based on quantiles is oft shown in comparative literature concerning L-moments. But why stop there? Why not compute the L-moments themselves to arbitrary order for
by either definition (the
uvlmoms
variation)? Why not fit a distribution to the computed L-moments for estimation of ? Or simply compute “skewness” according to the definition above (the
uvskew
variation).
Usage
uvlmoms(u,v=NULL, umv=TRUE, p=NA, type="gno", getlmoms=TRUE, ...)
uvskew( u,v=NULL, umv=TRUE, p=0.05, type=6, getlmoms=FALSE, ...)
Arguments
u |
Nonexceedance probability |
v |
Nonexceedance probability |
umv |
A logical controlling the computation of |
p |
A suggested |
type |
The |
getlmoms |
A logical triggering whether the L-moments of either |
... |
Additional arguments to pass to the lmomco function |
Value
An R list
of the univariate L-moments of is returned (see documentation for
lmoms
in the lmomco package). Or the skewness of can be either (1) based on the empirical distribution based on plotting positions by the
quantile
function in R using the type
as described, or (2) based on the fitted quantile function for the parameters of a distribution for the lmomco package.
Author(s)
W.H. Asquith
References
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.
See Also
Examples
## Not run:
set.seed(234)
UV <- simCOP(n=100, cop=GHcop, para=1.5, graphics=FALSE)
lmr <- uvlmoms(UV); print(lmr) # L-kurtosis = 0.16568268
uvskew(UV, p=0.10) # -0.1271723
uvskew(UV, p=0.10, type="gno") # -0.1467011
## End(Not run)
## Not run:
pss <- seq(0.01,0.49, by=0.01)
ETA <- sapply(1:length(pss), function(i) uvskew(UV, p=pss[i], type=5, uvm1=FALSE) )
plot(pss, ETA, type="l", xlab="P FACTOR", ylab="BIVARIATE SKEWNESS") #
## End(Not run)