# harris.exp.test: Harris modification of Gnedenko F-test In exptest: Tests for Exponentiality

## Description

Performs Harris modification of Gnedenko F-test for the composite hypothesis of exponentiality, see e.g. Ascher (1990).

## Usage

 1 harris.exp.test(x, R=length(x)/4, simulate.p.value=FALSE, nrepl=2000) 

## Arguments

 x a numeric vector of data values.
 R 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 test is based on the following statistic:

Q_n(R) =\frac{≤ft(∑_{i=1}^RD_i+∑_{i=n-R+1}^nD_i\right)/(2R)}{∑_{i=R+1}^{n-R}D_i/(n-2R)},

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, Q_n(R) has an F distribution with 4R and 2(n-2R) 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 "Harris modification of Gnedenko F-test". 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 harris.exp.test(rexp(100)) harris.exp.test(rlnorm(100)) 

### Example output

	Harris modification of Gnedenko's F-test

data:  rexp(100)
Q = 0.53946, p-value = 0.002255

Harris modification of Gnedenko's F-test

data:  rlnorm(100)
Q = 1.7407, p-value = 0.006013


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