# gini.exp.test: Test for exponentiality based on the Gini statistic In exptest: Tests for Exponentiality

## Description

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

## Usage

 1 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.

## Details

The test is based on the Gini statistic

G_n = \frac{∑_{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)).

## 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.

## Author(s)

Alexey Novikov, Ruslan Pusev and Maxim Yakovlev

## 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

 1 2 gini.exp.test(rexp(100)) gini.exp.test(runif(100, min = 0, max = 1)) 

### Example output

	Test for exponentiality based on the Gini statistic

data:  rexp(100)
Gn = 0.45513, p-value = 0.122

Test for exponentiality based on the Gini statistic

data:  runif(100, min = 0, max = 1)
Gn = 0.32778, p-value = 2.921e-09


exptest documentation built on May 1, 2019, 8:01 p.m.