asymmetry: Asymmetry / skewness measures for bivariate copulas

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Reflection and permutation asymmetry / skewness measures for bivariate copulas

Usage

skewrefl(uu)  # third moment (u1+u2-1)^3
skewperm(uu)  # third moment  (u1-u2)^3
qskewperm(uu,p=.05,nrep=100)  # quantile-based measure for u1-u2
qskewrefl(uu,p=.05,nrep=100)  # quantile-based measure for u1+u2-1

Arguments

uu	nx2 data matrix of uniform scores
p	value between 0 and 0.5, leading to quantiles at p and 1-p
nrep	number of replications for bootstrap SE

Value

skewness/asymmetry measure, with a crude SE

References

Rosco J-F and Joe H (2014). Measures of tail asymmetry for bivariate copulas. Statistical Papers, 54, 709-726.

Examples

n=100
set.seed(123)
urefl=rbreflasym(n,.25)  # extreme reflection asymmetry
uperm=rbpermasym(n,.25)  # extreme permutation asymmetry
n=1000
set.seed(123)
uagum=rbasymgum1(n,c(2,.4))  # bivariate asymmetric Gumbel
umo=rbMO1(n,p=.4) # bivariate 1-parameter Marshall-Olkin
## Not run: 
par(mfrow=c(2,2))
plot(urefl)
plot(uperm)
plot(uagum)
plot(umo) 
## End(Not run)
sk1=skewrefl(urefl)
sk2=skewperm(uperm)
skagum=skewperm(uagum)
skmo=skewperm(umo)
print(rbind(sk1,sk2,skagum,skmo))
qsk1=qskewrefl(urefl)
qsk2=qskewperm(uperm)
qskagum=qskewperm(uagum)
qskmo=qskewperm(umo)
print(rbind(qsk1,qsk2,qskagum,qskmo)) 

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.