KcopTest {Kcop}

Nonparametric smooth test for equality of copulas

Description

This functions performs the nonparametric smooth test to compare simultaneously K(K>1) copulas. See 'Details' below for further information.

Usage

KcopTest(Kdata, dn = 3, paired = FALSE)

Arguments

Kdata

A list of the K dataframe or matrix

dn

Number of copulas coefficients considered

paired

A logical indicating whether to consider the datas as paired

Details

Recall that we have K multivariate populations of arbitrary sizes, possibly paired with unknow associated copulas C_1,...,C_K respectively. KcopTest performs the following hypothesis H0: C_1=C_2=...=C_K against H1: C_l differs from C_m (l different from m and l,m in 1:K). The test is based on copulas cross-moments founded on Legendre polynomials that he called copulas coefficients. See the paper at the following HAL weblink: https://hal.archives-ouvertes.fr/hal-03475324v2

Value

A list with three elements: the p-value of the test, the value of the test statistic and the selected rank of copulas coefficients (number of terms involved in the test statistic)

Author(s)

Yves Ismael Ngounou Bakam

Examples

## simulation of 5 three-dimensional populations of different sizes
Packages <- c("copula","gtools","dplyr", "orthopolynom", "stats")
lapply(Packages, library, character.only = TRUE) # if necessary
set.seed(2022)
dat1<-rCopula(50, copula = gumbelCopula(param=6,dim = 2))
dat2<-rCopula(60, copula = claytonCopula(param=0.4,dim = 2))
dat3<-rCopula(55, copula = claytonCopula(param=0.4,dim = 2))
## Form a list of data
Kdata<-list(data1=dat1,data2=dat2,data3=dat3)
## Applying the test
KcopTest(Kdata = Kdata)