CV2 test of exponentiality

Description

Test of exponentiality based on the squared coefficient of variation.

Usage

   CV2.test(x, method = c("num", "sim", "asymp"), nSamp = 15000)

Arguments

Details

The distribution of CV^2 is that of Greenwood's statistic up to normalising constants. It approximately normal with expectation 1 and standard deviation 2/sqrt(n) for a large sample size n. Yet the convergence to the normal is known to be very slow.

Value

A list of test results.

Note

This test is sometimes referred to as Wilk's exponentiality test or as WE1 test. It works quite well for a Lomax alternative (i.e. GPD with shape ξ >0), and hence can be compared to Jackson's test and the Likelihood-Ratio (LR) test of exponentiality. However, this test has lower power that of the two others while having a comparable computation cost due to the evaluation of the Greenwood's statistic distribution.

Author(s)

Yves Deville

References

S. Ascher (1990) "A Survey of Tests for Exponentiality" Commun. Statist. Theory Methods, 19(5), pp. 1811-1525.

See Also

The function CV2 that computes the statistic and LRExp.test or Jackson.test for functions implementing comparable tests or exponentiality with the same arguments.

Examples

n <- 30; nSamp <- 500
X <- matrix(rexp(n * nSamp), nrow = nSamp, ncol = n)
pVals <- apply(X, 1, function(x) CV2.test(x)$p.value)
plot(pVals)  ## should be uniform on (0, 1)

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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Renext)
Loading required package: evd
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Renext/CV2.test.Rd_%03d_medium.png", width=480, height=480)
> ### Name: CV2.test
> ### Title: CV2 test of exponentiality
> ### Aliases: CV2.test
> 
> ### ** Examples
> 
> n <- 30; nSamp <- 500
> X <- matrix(rexp(n * nSamp), nrow = nSamp, ncol = n)
> pVals <- apply(X, 1, function(x) CV2.test(x)$p.value)
> plot(pVals)  ## should be uniform on (0, 1)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>