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 Moran statistic.
p.valuethe p-value for the test.
methodthe character string "Moran test for exponentiality".
data.namea character string giving the name(s) of the data.
Details
The Moran test for exponentiality is based on the following statistic:
$$T_n^+ = \gamma + \frac{1}{n}\sum_{i=1}^n{\log\frac{X_i}{\overline{X}}},$$
where $\gamma$ is Euler-Mascheroni constant.
The statistic is asymptotically normal: $$\sqrt{n}\,T_n^+ \to N\left(0,\frac{\pi^2}{6} - 1\right).$$
References
Moran, P.A.P. (1951): The random division of an interval--Part II. --- Journal of the Royal Statistical Society. Series B (Methodological), vol. 13, pp. 147-150.
Tchirina, A.V. (2005): Bahadur efficiency and local optimality of a test for exponentiality based on the Moran statistics. --- Journal of Mathematical Sciences, vol. 127, No. 1, pp. 1812--1819.