KLdiv: Kullback-Leibler divergence and sample size for two bivariate...
In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description Usage Arguments Value See Also Examples

Kullback-Leibler divergence and sample size for two bivariate copula densities

KLcopvsbvn(rho,dcop2,param2,copname2="bivcop",UB=7,iprint=F)
KLcopvscop(copname1="cop1",param1,dcop1,copname2="cop2",param2,dcop2,UB=7,iprint=F)
KL12gl(par2,dcop2,par1,dcop1,parlb=0,gl)
KLoptgl(dcop1,dcop2,par1,par2,name1,name2,par2lb=0,gl,pcop1,pcop2,
   ccdf1a,ccdf1b,ccdf2a,ccdf2b,prlevel=0)

`dcop1`	function for first bivariate copula density; form is dcop(u,v,param)
`dcop2`	function for second bivariate copula density
`copname1`	name of first bivariate copula density
`copname2`	name of second bivariate copula density
`rho`	parameter of dcop1 if it is bivariate normal
`param1`	parameter of dcop1
`param2`	parameter of dcop2
`UB`	limit to use for 2-dimensional integration with respect to bivariate normal density
`iprint`	print flag for intermediate results, FALSE by default
`par1`	copula parameter for family 1
`par2`	copula parameter for family 2
`parlb`	lower bound for copula parameter for family 2
`par2lb`	lower bound for copula parameter for family 2
`gl`	Gauss-Legendre quadrature object with $nodes and $weights
`name1`	name of first bivariate copula density
`name2`	name of second bivariate copula density
`pcop1`	function for first bivariate copula cdf; form is pcop(u,v,param)
`pcop2`	function for second bivariate copula cdf
`ccdf1a`	function for C_{2\|1} for pcop1
`ccdf1b`	function for C_{1\|2} for pcop1
`ccdf2a`	function for C_{2\|1} for pcop2
`ccdf2b`	function for C_{1\|2} for pcop2
`prlevel`	print.level for nlm

For KLcopvsbvn and KLcopvscop, a vector with 5 elements: KLcop1true, KLcop2true, Jeffreys, sampsize1, sampsize2, where KLcop1true (KLcop2true) is the KL divergence when copula 1 (respectively copula 2) is the true model; Jeffreys=KLcop1true+KLcop2true is Jeffreys' divergence, sampsize1 (sampsize2) is the sample size needed to distinguish with the other copula family wth probability 0.95 when copula 1 (respectively copula 2) is the true model.

For KL12gl, a single value for divergence; this function is optimized by KLoptgl.

For KLoptgl, a list with $cpar2 for the parameter of copula2 leading to small KL divergence with copula1 with parameter param1, $depm1=c(be1,tau1,rhoS1,rhoN1) is a vector of beta,tau,rhoS,rhoN for copula1 with parameter param1, $depm2=c(be2,tau2,rhoS2,rhoN12 is a vector of beta,tau,rhoS,rhoN for copula2 with parameter cpar2.

pcop pcond deppar2taurhobetalambda

rho=bvn.b2cpar(0.5)
par.gum=gum.b2cpar(0.5)
par.gal=gal.b2cpar(0.5)
KLcopvsbvn(rho,dcop2=dgum,param2=par.gum,copname2="Gumbel",UB=6,iprint=TRUE) 
KLcopvscop("Gumbel",par.gum,dgum,"Galambos",par.gal,dgal,UB=6,iprint=TRUE)
# parameter from Plackett family closed to bivariate Gaussian copula with 
#   rhoS=0.5 
cpar1=bvn.rhoS2cpar(.5)
cpar2=pla.rhoS2cpar(.5)  # 5.115661
gl25=gausslegendre(25)
kl=KLoptgl(dbvncop,dpla,cpar1,cpar2,"bvn","plackett",0,gl25,pbvncop,ppla,
   pcondbvncop,pcondbvncop,pcondpla,pcondpla)
print(kl$cpar2)  # 4.671857