# epstein.exp.test: Epstein test for exponentiality In exptest: Tests for Exponentiality

## Description

Performs Epstein test for the composite hypothesis of exponentiality, see e.g. Ascher (1990).

## Usage

 1 epstein.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 following statistic:

EPS_n =\frac{2n≤ft(\log≤ft(n^{-1}∑_{i=1}^nD_i\right)-n^{-1}∑_{i=1}^n\log(D_i)\right)}{1+(n+1)/(6n)},

where D_i=(n-i+1)(X_{(i)}-X_{(i-1)}), X_{(0)}=0 and X_{(1)}≤q…≤q X_{(n)} are the order statistics. Under exponentiality, EPS is approximately distributed as a chi-square with n-1 degrees of freedom.

## Value

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

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

## Author(s)

Alexey Novikov, Ruslan Pusev and Maxim Yakovlev

## References

Ascher, S. (1990): A survey of tests for exponentiality. — Communications in Statistics – Theory and Methods, vol. 19, pp. 1811–1825.

## Examples

 1 2 epstein.exp.test(rexp(100)) epstein.exp.test(rweibull(100,2)) 

exptest documentation built on May 29, 2017, 10:48 a.m.