Jackson.test: Jackson's test of exponentiality

Description

Jackson's test of exponentiality

Usage

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

Value

A list of results.

statistic, p.value

The statistic and \(p\)-value.

df

Number \(n\) of observations.

method

Description of the test implemented, regardless of how the \(p\)-value has been computed.

Arguments

x: numeric vector or matrix.
method: Character: choice of the method used to compute the \(p\)-value. See the Details section.
nSamp: Number of samples used to compute the \(p\)-value if method is "sim".

Author

Yves Deville

Details

Compute the Jackson's test of exponentiality. The test statistic is the ratio of weighted sums of the order statistics. Both sums can also be written as weighted sums of the scalings.

The Jackson's statistic for a sample of size \(n\) of the exponential distribution can be shown to be approximately normal. More precisely \(\sqrt{n}(J_n -2)\) has approximately a standard normal distribution. This distribution is used to compute the \(p\)-value when method is "asymp". When method is "num", a numerical approximation of the distribution is used. Finally, when method is "sim" the \(p\)-value is computed by simulating nSamp samples of size length(x) and estimating the probability to have a Jackson's statistic larger than that of the 'observed' x.

References

J. Beirlant and T. de Weit and Y. Goegebeur(2006) "A Goodness-of-fit Statistic for Pareto-Type Behaviour", J. Comp. Appl. Math., 186(1), pp. 99-116.

T.J. Kozubowski, A. K. Panorska, F. Qeadan, A. Gershunov and D. Rominger (2009) "Testing Exponentiality Versus Pareto Distribution via Likelihood Ratio" Comm. Statist. Simulation Comput. 38(1), pp. 118-139.

Examples

Run this code

set.seed(1234)
x <- rGPD(n = 50, loc = 0, scale = 1, shape = 0.1)
Jackson.test(x, method = "num")$p.value
Jackson.test(x, method = "asymp")$p.value
Jackson.test(x, method = "sim")$p.value

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