# atkinson.exp.test: Atkinson test for exponentiality In exptest: Tests for Exponentiality

## Description

Performs Atkinson test for the composite hypothesis of exponentiality, see e.g. Mimoto and Zitikis (2008).

## Usage

 1 atkinson.exp.test(x, p=0.99, simulate.p.value=FALSE, nrepl=2000) 

## Arguments

 x a numeric vector of data values.
 p a parameter of the test (see below). 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 Atkinson test for exponentiality is based on the following statistic:

T_n(p) = √{n}≤ft| \frac{≤ft(n^{-1}∑_{i=1}^n{X_i^p}\right)^{1/p}}{\overline{X}} -(Γ(1+p))^{\frac{1}{p}}\right|.

The statistic is asymptotically normal: T_n(p) \to ≤ft| N(0,σ^2(p))\right|, where

σ^2(p) = ≤ft(Γ(1+p)\right)^{\frac{2}{p}}≤ft( -1 - \frac{1}{p^2} + \frac{Γ(1+2p)}{p^2Γ^2(1+p)}\right).

## Value

A list with class "htest" containing the following components:

 statistic the value of the Atkinson statistic. p.value  the p-value for the test. method the character string "Atkinson test for exponentiality". data.name a character string giving the name(s) of the data.

## Author(s)

Alexey Novikov and Ruslan Pusev

## 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.

## Examples

 1 2 atkinson.exp.test(rexp(100)) atkinson.exp.test(rchisq(100,3)) 

### Example output

	Atkinson test for exponentiality

data:  rexp(100)
T = 0.006994, p-value = 0.1928

Atkinson test for exponentiality

data:  rchisq(100, 3)
T = 0.015745, p-value = 0.00337


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