cvm.exp.test: Cramer-von Mises test for exponentiality
Description
Performs Cramer-von Mises test for the composite hypothesis of exponentiality,
see e.g. Henze and Meintanis (2005, Sec. 2.1).
Usage
cvm.exp.test(x, nrepl=2000)
Arguments
x
a numeric vector of data values.
nrepl
the number of replications in Monte Carlo simulation.
Value
A list with class "htest" containing the following components:
statisticthe value of the Cramer-von Mises statistic.
p.valuethe p-value for the test.
methodthe character string "Cramer-von Mises test for exponentiality".
data.namea character string giving the name(s) of the data.
Details
The Cramer-von Mises test for exponentiality is based on the following statistic:
$$\omega^2_n =\int_0^\infty (F_n(x)-(1-\exp(-x)))^2\exp(-x)dx,$$
where $F_n$ is the empirical distribution function of the scaled data $Y_j=X_j/\overline{X}$. The p-value is computed by Monte Carlo simulation.
References
Henze, N. and Meintanis, S.G. (2005): Recent and classical tests for exponentiality: a partial review with comparisons. --- Metrika, vol. 61, pp. 29--45.