iprlma171
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R version 3.0.2 (2013-09-25) -- "Frisbee Sailing"
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> ## load the package and the data
> library(copula)
> data(loss)
> 
> ## select uncensored claims
> myLoss <- subset(loss, censored==0, select=c("loss", "alae"))
> 
> ## there are many ties in the data
> nrow(myLoss)
[1] 1466
> sapply(myLoss, function(x) length(unique(x)))
loss alae 
 541 1401 
> 
> ## let us break the ties "at random"
> set.seed(123)
> pseudoLoss <- sapply(myLoss, rank, ties.method="random") / (nrow(myLoss) + 1)
> 
> ## extreme-value dependence tests
> evTestK(pseudoLoss)

	Test of bivariate extreme-value dependence based on Kendall's process
	with argument 'method' set to “fsample”

data:  pseudoLoss
statistic = -0.1453, p-value = 0.8845

> evTestC(pseudoLoss)

	Max-stability based test of extreme-value dependence for multivariate
	copulas

data:  pseudoLoss
statistic = 0.1469, p-value = 0.468

> evTestA(pseudoLoss, derivatives="Cn")

	Test of bivariate extreme-value dependence based on the CFG estimator
	with argument 'derivatives' set to 'Cn'

data:  pseudoLoss
statistic = 0.0186, p-value = 0.4231

> 
> ## exchangeability test
> exchEVTest(pseudoLoss)

	Test of exchangeability for bivariate extreme-value copulas with
	argument 'estimator' set to 'CFG', argument 'derivatives' set to 'Cn'
	and argument 'm' set to 100

data:  pseudoLoss
statistic = 0.0751, p-value = 0.1653

> 
> ## goodness-of-fit test
> gofEVCopula(gumbelCopula(), pseudoLoss, method="itau", verbose=FALSE)

	Parametric bootstrap based GOF test for EV copulas with argument
	'method' set to 'itau' and argument 'estimator' set to 'CFG'

data:  pseudoLoss
statistic = 0.0377, parameter = 1.44, p-value = 0.2592

> 
> ## fit the Gumbel-Hougaard family
> fitCopula(gumbelCopula(), pseudoLoss, method="itau")
fitCopula() estimation based on 'inversion of Kendall's tau'
and a sample of size 1466.
      Estimate Std. Error z value Pr(>|z|)    
param  1.44040    0.03327   43.29   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> ## study the effect of the randomization
> randomize <- function()
+ {
+     pseudoLoss <- sapply(myLoss, rank, ties.method="random") / (nrow(myLoss) + 1)
+     evtK <- evTestK(pseudoLoss)$p.value
+     evtC <- evTestC(pseudoLoss)$p.value
+     evtA <- evTestA(pseudoLoss, derivatives="Cn")$p.value
+     exevt <- exchEVTest(pseudoLoss)$p.value
+     gofevGH <- gofEVCopula(gumbelCopula(), pseudoLoss, method="itau", verbose=FALSE)$p.value
+     fitGH <- fitCopula(gumbelCopula(), pseudoLoss, method="itau")
+     c(evtK=evtK, evtC=evtC, evtA=evtA, exevt=exevt, gofevGH=gofevGH,
+       est=fitGH@estimate, se=sqrt(fitGH@var.est))
+ }
> 
> ## replicate 100 times
> #reps <- t(replicate(100, randomize()))
> #round(apply(reps, 2, summary),3)
> 
> ## ignoring the ties can be bad
> pseudoLoss <- pobs(myLoss)
> evTestK(pseudoLoss)

	Test of bivariate extreme-value dependence based on Kendall's process
	with argument 'method' set to “fsample”

data:  pseudoLoss
statistic = 0.5219, p-value = 0.6017

> evTestC(pseudoLoss)

	Max-stability based test of extreme-value dependence for multivariate
	copulas

data:  pseudoLoss
statistic = 0.4005, p-value = 0.01648

> evTestA(pseudoLoss, derivatives = "Cn")

	Test of bivariate extreme-value dependence based on the CFG estimator
	with argument 'derivatives' set to 'Cn'

data:  pseudoLoss
statistic = 0.092, p-value = 0.0004995

> exchEVTest(pseudoLoss)

	Test of exchangeability for bivariate extreme-value copulas with
	argument 'estimator' set to 'CFG', argument 'derivatives' set to 'Cn'
	and argument 'm' set to 100

data:  pseudoLoss
statistic = 0.0814, p-value = 0.1174

> gofEVCopula(gumbelCopula(), pseudoLoss, method="itau", verbose=FALSE)

	Parametric bootstrap based GOF test for EV copulas with argument
	'method' set to 'itau' and argument 'estimator' set to 'CFG'

data:  pseudoLoss
statistic = 0.0476, parameter = 1.446, p-value = 0.1783

> fitCopula(gumbelCopula(), pseudoLoss, method="itau")
fitCopula() estimation based on 'inversion of Kendall's tau'
and a sample of size 1466.
      Estimate Std. Error z value Pr(>|z|)    
param  1.44645    0.03318   43.59   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>