It compute the JLn-statistic, from a bivariate sample of continuous random variables X and Y.
Usage
JLn(x, y)
Arguments
x, y
numeric vectors of data values. x and y must have the same length.
Details
See subsection 3.2.-Main reference. For sample sizes less than 20, the correction introduced in subsection 3.2 from main reference, with c = 0.4 was avoided.
Value
The value of the JLn-statistic.
Author(s)
J. E. Garcia and V. A. Gonzalez-Lopez
References
J. E. Garcia, V. A. Gonzalez-Lopez, Independence tests for continuous random variables based on the longest increasing subsequence, Journal of Multivariate Analysis (2014), http://dx.doi.org/10.1016/j.jmva.2014.02.010
Examples
## mixture of two bivariate normal, one with correlation 0.9 and
## the other with correlation -0.9
#
N <-100
ro<- 0.90
Z1<-rnorm(N)
Z2<-rnorm(N)
X2<-X1<-Z1
I<-(1:floor(N*0.5))
I2<-((floor(N*0.5)+1):N)
X1[I]<-Z1[I]
X2[I]<-(Z1[I]*ro+Z2[I]*sqrt(1-ro*ro))
X1[I2]<-Z1[I2]
X2[I2]<-(Z1[I2]*(-ro)+Z2[I2]*sqrt(1-ro*ro))
plot(X1,X2)
# calculate the statistic
a<-JLn(X1,X2)
a
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
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Type 'demo()' for some demos, 'help()' for on-line help, or
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> library(LIStest)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LIStest/JLn.Rd_%03d_medium.png", width=480, height=480)
> ### Name: JLn
> ### Title: JLn statistic, to test independence
> ### Aliases: JLn
> ### Keywords: ~longest increasing subsequence ~copula
>
> ### ** Examples
>
> ## mixture of two bivariate normal, one with correlation 0.9 and
> ## the other with correlation -0.9
> #
> N <-100
> ro<- 0.90
> Z1<-rnorm(N)
> Z2<-rnorm(N)
> X2<-X1<-Z1
> I<-(1:floor(N*0.5))
> I2<-((floor(N*0.5)+1):N)
> X1[I]<-Z1[I]
> X2[I]<-(Z1[I]*ro+Z2[I]*sqrt(1-ro*ro))
> X1[I2]<-Z1[I2]
> X2[I2]<-(Z1[I2]*(-ro)+Z2[I2]*sqrt(1-ro*ro))
> plot(X1,X2)
>
> # calculate the statistic
> a<-JLn(X1,X2)
> a
[1] 23.64151
>
>
>
>
>
>
> dev.off()
null device
1
>