# hollander.exp.test: Hollander-Proshan test for exponentiality In exptest: Tests for Exponentiality

## Description

Performs Hollander-Proshan test for the composite hypothesis of exponentiality, see Hollander and Proshan (1972).

## Usage

 1 hollander.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:

J_n = \frac{1}{n(n - 1)(n - 2)}\, ∑_{i\ne j,k; j<k}1\{x_i > x_j+x_k\}.

Under exponentiality, one has

√{n}(J_n-\frac{1}{4})\stackrel{d}{\rightarrow}\mathcal N≤ft(0,frac{5}{432}\right).

(see Hollander and Proshan (1972)).

## 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 "Hollander-Proshan test for exponentiality". data.name a character string giving the name(s) of the data.

## Author(s)

Alexey Novikov and Ruslan Pusev

## References

Hollander M., Proshan F. (1972): Testing whether new is better than used. — Ann. Math. Stat., vol. 43, pp. 1136–1146.

## Examples

 1 2 hollander.exp.test(rexp(25)) hollander.exp.test(rgamma(25,2)) 

### Example output

	Hollander-Proshan test for exponentiality

data:  rexp(25)
T = 0.22203, p-value = 0.1936

Hollander-Proshan test for exponentiality

data:  rgamma(25, 2)
T = 0.08971, p-value = 9.37e-14


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