CV2 test of exponentiality

Test of exponentiality based on the squared coefficient of variation.

Usage

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

Arguments

x

Numeric vector giving the sample.

method

Method used to compute the \(p\)-value. Can be "asymp", "num" or "sim" as in LRExp.test.

nSamp

Number of samples used to compute the \(p\)-value when method is "sim".

Value

A list of test results.

statistic, p.value

The test statistic, i.e. the squared coefficient of variation \(\textrm{CV}^2\) and the \(p\)-value.

df

The sample size.

method

Description of the test method.

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 \(\xi >0\)), 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.

Details

The distribution of \(\textrm{CV}^2\) 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.

References

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

Author

Yves Deville

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)