# moran.exp.test: Moran test for exponentiality In exptest: Tests for Exponentiality

## Description

Performs Moran test for the composite hypothesis of exponentiality, see e.g. Moran (1951) and Tchirina (2005).

## Usage

 1 moran.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 Moran test for exponentiality is based on the following statistic:

T_n^+ = γ + \frac{1}{n}∑_{i=1}^n{\log\frac{X_i}{\overline{X}}},

where γ is Euler-Mascheroni constant. The statistic is asymptotically normal:

√{n}\,T_n^+ \to N≤ft(0,\frac{π^2}{6} - 1\right).

## Value

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

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

## Author(s)

Alexey Novikov and Ruslan Pusev

## 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.

## Examples

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

### Example output

	Moran test for exponentiality

data:  rexp(100)
T = 0.025411, p-value = 0.7517

Moran test for exponentiality

data:  rchisq(100, 3)
T = 0.19745, p-value = 0.01395


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