a logical value indicating whether to compute p-values by Monte Carlo simulation.
nrepl
the number of replications in Monte Carlo simulation.
Value
A list with class "htest" containing the following components:
statisticthe value of the Atkinson statistic.
p.valuethe p-value for the test.
methodthe character string "Atkinson test for exponentiality".
data.namea character string giving the name(s) of the data.
Details
The Atkinson test for exponentiality is based on the following statistic:
$$T_n(p) = \sqrt{n}\left| \frac{\left(n^{-1}\sum_{i=1}^n{X_i^p}\right)^{1/p}}{\overline{X}} -(\Gamma(1+p))^{\frac{1}{p}}\right|.$$
The statistic is asymptotically normal: $T_n(p) \to \left| N(0,\sigma^2(p))\right|$, where
$$\sigma^2(p) = \left(\Gamma(1+p)\right)^{\frac{2}{p}}\left( -1 - \frac{1}{p^2} + \frac{\Gamma(1+2p)}{p^2\Gamma^2(1+p)}\right).$$
References
Mimoto, N. and Zitikis, R. (2008): The Atkinson index, the Moran statistic, and testing exponentiality. --- J. Japan Statist. Soc., vol. 38, pp. 187--205.