exptest (version 1.2)

gini.exp.test: Test for exponentiality based on the Gini statistic

Description

Performs test for the composite hypothesis of exponentiality based on the Gini statistic, see e.g. Gail and Gastwirth (1978).

Usage

gini.exp.test(x, simulate.p.value=FALSE, nrepl=2000)

Arguments

x

a numeric vector of data values.

simulate.p.value

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:
• statistic
  the value of the Gini statistic.
• p.value
  the p-value for the test.
• method
  the character string "Test for exponentiality based on the Gini statistic".
• data.name
  a character string giving the name(s) of the data.

Details

The test is based on the Gini statistic $$G_n = \frac{\sum_{i,j=1}^n |X_i-X_j|}{2n(n-1)\overline{X}}.$$ Under exponentiality, the normalized statistic $(12(n-1))^{1/2}(G_n-0.5)$ is asymptotically standard normal (see, e.g., Gail and Gastwirth (1978)).

References

Gail, M.H. and Gastwirth, J.L. (1978): A scale-free goodness-of-fit test for the exponential distribution based on the Gini statistic. --- J. R. Stat. Soc. Ser. B, vol. 40, No. 3, pp. 350--357.

Examples

gini.exp.test(rexp(100))
gini.exp.test(runif(100, min = 0, max = 1))